What should I do as cross-training for running? (more details below)?

I’m a sophomore in high school. I ran winter and spring track freshman year. I didn’t do cross country (long story), but I’ve been training since the beginning of August.

Winter track started Monday.
My left leg is okay, but I have a shin splint and strained hamstring in my right leg. I know what to do for my shin splint and hamstring, but the athletic trainer said I should cross-train over the weekend.

I know swimming and biking are really common cross-training activities for running. I can’t ride a bike. I might be able to get to an indoor pool, but if I can’t get to a pool, what should I do tomorrow as cross-training?

Should I rest after track before training for cross country?

I run cross country, winter and spring track and I just ended spring track today. I run the mile if that helps at all. Should I rest at all before starting training for cross country? It starts at the end of August.

Should I train for running during the summer as if it was another season?

I’m a high school track & field/cross country funner and I feel that I’m not getting any faster. I was planning on training for a 2month season after 2 weeks of break from spring track and then get a 2 week break from the summer season before running cross country. Would it help or hurt me?
Also, should I or should I not train for speed and why?

How long does it take to lose stamina for running?

For the past month or so I have been doing sprinting/mid distance runs at about the difficulty of 75% of a high school spring track workout (if you can imagine what that is). I have run roughly every other day for about 40 days, and I have definitely been improving. How many consecutive days without running do I have to undergo before I start to lose stamina?

How do I start running to train for track?

I mean how far should I run since I am beginning? When is the best time to run? I plan on running winter and spring track. I am kind of afraid to run around my neighborhood because the men look perverted.