As a heads-up, this may be a bit long, and I'm not sure how to summarize it so I'm afraid there'll be a wall of text and no TL;DR. Sorry 'bout that.
So, I've spent quite a while playing, and developed myself into a small bit of a jack of all trade, and while I'm not overall qualified to give advice, I thought you might find it helpful nevertheless to hear my two cents.
1) The two biggest marks of Jungler efficiency as I've seen so far is Clear Speed, and Gank Frequency. Improving your clear speed can be somewhat difficult, as it involves several factors; basic abilities, items, (currently) Smite buffs, and so on. The best way to optimize clear speed that I know of involves this:
1. Choose your first camp based on your champion; While Smite buffs are still around, choosing your first camp can help a lot. The usual camps I take are Gromp for Mages and Tanks/Juggernauts (Champions like Fiddlesticks, Sejuani, etc.), and Krugs for high-attack speed champions (Xin Zhao and Master Yi being good examples.) - it may take some time to find out which camps work for you, but I'm certain if you work towards it, you'll get it down.
2. Experiment with Basic Abilities priorities; As anyone would know, and I know you're no exception, the basic abilities you choose first in order (and, even moreso, which ones you max first) can impact your clearing speed as well. Kha'Zix, for example, could take (Q) Taste Their Fear first for extra solitary power (as well as being able to take Gromp easier), or take (W) Void Spikes for early stability due to the heal.
3. Figuring out what items help clear speed the most; it may go without saying, but I know for some people it can be an issue, but Junglers can optimize around their clearing over ganking and still be a terror to see show up in lane. While more often than not, just buying out your Jungle item and Enchantment suffices, some Champions may need a little extra work to get their clears up to snuff. I wouldn't myself have any recommendations, so it's wholly up to personal study and practice to nail it.
As for gank frequency, that's also partly measured by some other factors, like gank pressure, successes, and map awareness. In some cases, you won't be generally successful with a gank; your ally might die and your target will get away, or the enemy Jungler will be just near enough to counter-gank, and so forth and so on.
Gank Pressure - Being brutally honest, there's no real way to apply gank pressure without being an extremely mobile champion (like Hecarim), or without being a champion with a unique mechanic (Ivern's Brushmaker, Kindred's Mark of the Kindred), and without stuff like that, your biggest method of keeping pressure is to camp. Nobody's going to like it, but it often has to be done.
Map Awareness - Another necessity in the Jungle is keeping your eye on the map as much as possible. Between all five roles, the Jungler must make the best use of the map for tactical purposes. Ganking a lane that's pushed up often won't yield any results, whereas ganking a lane that you see your ally starting to fail on would likely benefit you more. (This also plays in to gank pressure; if you see an ally dropping to low health constantly in-lane, you're probably going to want to camp that person out.)
Defining "Success" - One of the most aggravating parts of Jungling is ganking and coming short of what would have otherwise been a good gank, and sometimes you'll only be able to come in and perform clean-up detail after your ally dies. When it comes to defining success, I personally prioritize like this; Personal survival > Ally survival > Enemy death > Pushing. It sure as hell ain't perfect, but keeping such a mindset helps soften the impact of a normally bad gank.
Bonus Points: Objectives - The other big thing that Junglers do is usually marked near the corners of the map; taking Dragon, Rift Herald, and Baron Nashor. And often, you won't be able to take those objectives alone, so the only option is to free up your allies with a gank and request help. Just bear in mind that this may very well garner the attention of other lanes and the enemy Jungler.
As for keeping your health during clearing, that's a difficult thing in general. You'll probably only get so far with it, but I often use Health Potions (I don't particularly see the use in Refillable Potions going into Hunter's Potion) and - in the cases where I'm starting with Krugs - I often reserve my second Smite for the Brambleback.
2) Keeping a lead is often hard, but just having it increases the chances you'll keep it. (note; the following may likely not qualify as valid advice because the majority of my time top lane has been spent as Yorick. Take this with a grain of salt.) Once you have a lead, keep your general points of entry warded; having a kill lead over your opponents means you're growing to become a target for every last member of the enemy team. Knowing where your opponents are coming from will help the most, since you'll be able to decide whether or not you can take them on.
One good tactic that I like to use is to bait out ganks; push up slightly, and wound your opponent - preferably just below or around the 40% mark. Unless their Jungler is either too smart or too stupid, there's a good chance they'll gank you to give their ally the "surprise" edge - wherein you'll stop holding back on your opponent and then turn on the Jungler after they're dead. It's really fun to pull off.
3) Getting behind sucks, especially against champions like Darius and Riven who are notorious for chunking down people's health bars regardless of class. The only advice I can give is to be careful, keep vision (as with 2, giving a kill lead makes you as much a target as when you're getting one), and avoid confrontation with your opponents for until your Jungler shows up.
Depending on your opponent, you may actually want to get more aggressive. Taking Darius as an example, you can actually screw with him by doing some aggressive hit-and-run tactics; rush in, close on him until his Decimate can't heal him, do as much as you can in close quarters (Poppy's Iron Ambassador and Hammer Shock can work well enough), and then jump out before you reach max Hemorrhage stacks. (may be a little easier said if he has yet to use his _Apprehend). Just know your opponent, and advise yourself as to whether or not you should go on the defensive and focus creeps, or go on the offensive and fight back.
4) Mobile champions are definitely hard to deal with, especially those like Talon and Katarina with instant-movement engage tools (like Shunpo and Cutthroat), and in terms of combating them, often the only two things that can help are Crowd Control and threat of extreme damage. Aurelion may seem like one of the biggest victims of Assassins, but he can actually play around them with a little work and a little knowledge. Aiming to land Star Surge and Celestial Expansion are often his biggest tools (and only tools, for that matter) until he reaches 6.
But, in overall terms of fighting Assassins (and mobile champions in general) is to apply Crowd Control as frequently as possible. As for Jungling and having your opponent slip away, that is a twofold thing - one, I can refer to the priority list above for gank success, and two; pay close attention to the mobile champions. Most mobile champions on bottom lane (with the exception of Sivir and Jinx) have a dash ability; if you see it used, that's roughly when you should gank, if possible.
I apologize that this was so long, but I hope it helped you!