It is excellent to be curious and ask lots of questions. You should always do this with your training and in life in general.
Many of your questions pile on top of one another and get a little complicated. I'll try to answer them as best I can. But first I have a general response. Just run. Spend most of your time running easy and slowly increase the amount of time you spend running in any given week. Don't stress about pace or mileage. Think about piling up 30 minute runs, or 45 minute runs, or getting to an hour of easy, continuous running. It sounds like you have a coach and do some races, that is perfect for now.
General consensus on a long run is once a week or once every other week. Long is relative and it will end up being the longest run you do in that 1-2 week period. Recovery runs are extra slow and extra short and should be done after a race or really hard effort or when you're feeling tired and beat up (although a day off is also good in these moments).
I count all running in my log. Warm ups, cool downs, etc. You can do it however you want to. But you're running these, right? So they count.
If your coach has you doing a specific warm up, you should probably just do that. In time you will most likely spend more time on warm ups.
Strength training is almost always a good idea. I like one of two options. One, develop a simple daily routine of stretches, calisthenics, and bodyweight moves and do them near daily. Do these in the evening if you run in the morning (or the opposite). Two, develop a more comprehensive strength routine that includes weights and do this 2-3 times a week. Honestly in your position, I'd just go with number one to get used to it all.
Hills are always good. Running over hilly terrain will make your stronger pretty much always. In many runners base phases, that is enough (if you're curious about this read up on the training of Mark Nenow). Hill training specifically can also be good, doing 6-10 reps of a short hill at a strong effort once a week will help. Should you increase this during base? This is one of those questions that gets really complicated. The simple version is to just run over hills sometimes, don't stress about it. As your training progresses (I'm talking years, not weeks) you will get more specific about things like this. For now, just keep running.
It's going to be summer, just run no matter what the temp is. Don't worry about doing it for heat acclimation or whatever. Just run.
Your training plan is like I said above. Run a lot. Most of it easy. Work with your coach when you have one. Over the course of the summer work to increase the number of days per week you run, and the number of minutes you spend on each run. Don't worry about what the miles are.