I am training for a hilly half marathon. I am near enough to the race course to run it during training. I am trying to incorporate the hilly part of the course at least once per week.
I believe that doing lunges and squats would also benefit my training. I have seen other threads about doing them. However, I have not seen any advice about when to do them? I generally run 4 days a week, 2 cross training days, and one rest day. Should I do the lunges/squats on a run day or cross training day? I am concerned if I do them on cross training day that I am not really resting my legs, but am open to hear what others think. If I do them on run days, I assume it would be in conjunction with a shorter run, not long run day.
In my experience strength exercises that target the posterior chain are more beneficial for running than those that target the quads. Squats and lunges don't recruit the hamstrings as much as deadlifts or hamstring curls. Glutes are also important and benefit from glute bridge and hip thrusts.
Kettlebell swings are also great for the posterior chain. I incorporate them into my workouts about twice per week. If I plan a long and hard run, I don't do them the day before. I am not sure that exercise gurus would recommend the way that I do kettlebell swings but I usually do them "tabata style." I do 20 seconds of swings with a 10 second rest and repeat that 8 times. I concentrate more on using good form than trying to crank out as many as I can in that 20 seconds. I usually get 10-12 reps and use a 35 pound kettlebell. That will get your HR & RR up and is a great hamstring workout.
Two other hamstring workouts I'll do, but I don't like them as much as KB swings, are hamsting "bunouts" and hamstring lifts. I am not sure what the real names of the exercises are but that is what I call them. I do these because I don't like hamstring curls.
On "burnouts" I kneel on a carpeted floor with my feet against the wall and facing away from the wall. I lean forward, bending at the knee, as far as I can without falling forward. I try to hold it in that position as long as possible. I just repeat that a few time.
I have gymnastics rings in my basement that I can lower. I lower them to a spot that I can put my feet through them while on my back. They're off of the floor so that when I lift up my legs at the hips, my lower leg is about parallel to the ground. I then lift my butt up off of the floor and hold it for about 30 seconds. I repeat that maybe 6-8 times and do crunches in between sets with my feet still through the rings. Another similar exercise to this is a leg curl with a physio ball. I do this one leg at a time.
I'll also disclose that I am more of cyclist than a runner depending on the time of the year. I'm usually about 75% on the bike and 25% running but sometimes that shifts more to running.
Saying "squats and lunges don't recruit the hamstrings as much as deadlifts or hamstring curls" is pretty short sighted and borderline wrong - maybe if you're only doing front squats. Try doing low bar squats and tell me your hamstrings aren't being recruited. And back squats do work the posterior chain as well.
HOWEVER, not going to neg you here about encouraging posterior chain development. It's definitely severely underutilized with runners and, at bare minimum, greatly helps prevent hip related injuries. Fact is, most runners would benefit from just incorporating some sort of heavy(ish) squatting and deadlifting.
With that said, based on your post, I'd recommend running at least 6 days a week and do some hill workouts if you're worried about the hills. That will help this specific ask more than anything.
Do Back Squats recruit the posterior chain? Yes. Do other exercise focus more on the posterior chain? Yes.
For new lifters who I don't have any contact with I always suggest doing cross arm Front Squats and Trap Bar Deadlifts. They are variations of squatting and hinging movements which require very little coaching and are hard to perform incorrectly.
"Hamstring curls" do not work your hamstrings in the way they are useful for running. If you want to make this exercise running specific, what you need to do is "reverse hamstring curls." Set the weight at about half of what you would do in a regular curl, lift the bar with two legs, and then lower the bar slowly with one leg. Your hamstring should work harder in an eccentric motion because that's when the force is applied while you are running.