Will practicing against intermediate bots make me better?

No, only playing against Players will help you get better. Bots are too predictable and easily manipulated, and they will never have the intelligence level of an actual person.

Yes, but depends on what you want to work on. Like bots are better for practicing jungle routes since the creeps level up more realistically as the game progresses (they scale with the average of all player levels). Bots are a less risky way to practice complicated maneuvers like towerdiving with and practicing his passive blocking tower shots. It's also a low pressure environment for practicing mechanics with other players in the mix.

Bots are horrible for practicing skillshots since the bots move differently than players. Not as good for dueling since they're less aggressive and will stop damage mid combo even if they could kill you. So not good for everything, but great for practicing some things.

It helps you with understanding the basic mechanics of your champion, what combos you can do etc. You can possibly train jungle paths. But it doesn't help for a lot of things : playing under pressure/ jungle pressure, trading against someone that knows what he's doing, how the matchups go when you're not fed, when to roam, the objectives importance, etc.

It does help for a very new player, but soon gets vastly outclassed by other kind of games.

Once you get to a certain point, AI is useful for win of the day and for trying out a new champion. Beyond that, they don't act much like real players.

It's great for practicing things like last-hitting and timing the jungle, because they don't put much pressure on anyone, unless you're unlucky enough to go solo top. It's also great for learning the feel of a champion's kit. Other than that, you get better by beating other players.

Only for practicing management of using your time and spells between harassing and CSing. That's about it.

Practice CS against bots for sure as they will harass you, but for trades in lane, they aren't good for learning.

No.

Call me Captain Obvious, but if you're regularly beating Intermediate Bots, they've ceased to be helpful to you.

If you can last hit reliably enough, and you can harass the Bots, stop practicing against them for anything other than your first pass at a new champion.

Depends on your level of skill, yes if you are a newby, no if you can reliably beat them with 0 deaths.