Sometimes during the laning phase I feel like I'm glued to the botlane. Is my job really to just keep the tower alive, shut down enemy botlane and control dragon, or is there more that I can do, when and how (in lower elo)?
Also, what are some good adc picks for low elo?
are all good low elo picks. 
is a little trickier but she's a insane hypercarry late game. In general you want to get the enemy tower down first and then just start roaming or if you're just destroying bot lane, force the issue and make them come down and stop your from taking 2nd tier turrets.
I find ADCs who control their lane and push their advantage down bot lane do better than ADCs who just let off the pressure and start teaming up too early.
Take all this with a grain of salt...
The biggest problem in lower elo is figuring out when to actually leave the bottom lane. I've had it described to me by a diamond player, that If one of the turrets is down (yours or theirs), then it is time to start checking the map regularly for other activity. You can stay in bot lane, but remember: if you overstay, then you and your support could be easily picked off, the dragon/baron/rift herald could be easily grabbed and/or other laners could be mowed down.
Another thing to note is that at about the 8-10 minute mark, you can usually sense that the game is starting to shift gears towards more team fights - another clue that maybe it is time to re-assess your position.
If no first tower blood has been drawn and the tower is pretty health you typically continue in "laning" phase.
It sounds like you have a hard time figuring out when laning phase ends, rather than figuring out when to stop protecting a tower.
Depending on your champion laning goes roughly 15 minutes, but it continues longer in lower elo. On my smurf account I played a game that had a 30 minute laning phase. No one would leave their lane.
When towers get to be less that half health, you should stop protecting them. You will probably get dove protecting a tower that is on its last leg.
You and your support will die and THEN you will lose the tower as well.
Sometimes during the laning phase I feel like I'm glued to the botlane. Is my job really to just keep the tower alive, shut down enemy botlane and control dragon, or is there more that I can do, when and how (in lower elo)?
Also, what are some good adc picks for low elo?
your job is to get as fed as possible as soon as possible, that is it, you don't leave lane to roam unless there's a guaranteed free kill right in the river, or to defend a dragon intelligently. in low elo caitlyn, lucian, sivir, miss fortune are all good
avoid vayne, jinx, jhin unless you can hit W every time, corki, ezreal again unless you can land every Q and have great coordination, kalista(47% winrate, the community is lying to themselves saying she is any good)
every champion requires intensive and extensive training to master, then you must master positioning, trading, csing, various trading while csing techniques, match ups, when you're stronger, when you're not, it's why 90% of the player base is below high silver, the game takes a lot of time to be really good at.
You really don't have any business roaming unless there is an easy kill in the jungle or to provide presence to help a teammate escape. Otherwise, sit in your lane and farm, trade, and take tower. When I play support, I expect my adc to be cs'ing unless I go in for a trade. From what iv'e seen, low elo has a problem with cs'ing. If you can farm really well you will almost always come out on top when it matters unless the other adc gets fed off complacency. If you can get tower early, then do it and grab tower first blood. After that I usually go mid to get that tower to keep the map pressure. Understand what your 2-3 item power spikes are and use them to your advantage. Also, know when to back out of a fight. If you can survive early game, you will be valuable mid/late game as that is when your damage really comes out.
pick someone who doesn't rely on a support, and can do well enough in lane phase. avoid hyper carries such as vayne and kog because your team will throw you to the rengars
Agree with almost everything here, except that Vayne is a bad low elo pick.
In low elo, most players don't have the know-how to abuse Vayne's low range and awkward W-proc trading, so you can either farm safely or outplay their aggression, depending on the matchup. Additionally, on relatively equal farm, Vayne can duel almost any adc the instant she hits 6.
Vayne also thrives in the chaos of low elo teamfights. Low elos don't properly use sweepers/pink wards to counter your ultimate, and don't coordinate their dives to work around your initial E self-peel, so you can generally rampage around teamfights for free.
Finally, low elo games go on much longer than they should, and Vayne is one of the best and most reliable late game ADCs.
