I have an alpha trainer 40 with a JR 700 mah battery. Can I charge this with my superbrain 959 peak charger at .5 amps w/o hurting the batt?

yes,

You could probably get away with 1 amp or 1.5 amps, but if you have the time, just go slow.

Batteries prefer a slow charge so use the wall-wart when you can.

I usually do a 15 hr wall-wart charge the day before I fly then if need to top off at the field I use my fast charger set to 1 amp.
also the fast charger comes in handy if you unexpectedly get a chance to fly and didn't charge your RX pack. My next inverstment will be a fast charger for my TX. any suggestions.

G'day Mate,
The best charge rate for that pack would be 70ma, that's 0.07 amps, not 0.7A which is 700ma.
Slow is best, too fast & the cells will build up gas which causes them to vent, & loose electrolyte, which kills em real quick.

So I should probably buy a second batt and have them both charged slowly if expecting alot of flight time. How many flights should I get off one 700mah batt.

G'day Mate,
It's a good idea to cycle new battery packs, talk to your mates at the field & beg or borrow a cycler, after 3 or 4 cycles with slow charging, your battery capacity should improve to about 96 to 99% of it's rated 700Mah.
That should be enough with a trainer to fly all day, but use a loaded battery tester, between flights, to keep track of your battery condition.

Number of flights will vary based on a lot of things.

Number of servos
Type of servos - analog or digital
Time with radio on but not flying - tuning, tweaking controls or "oops, I left my radio turned on".
Drag/resistance in control systems including any stalled conditions
Voltage and capacity of battery pack as well as condition of that pack
Flight loads and style of flying

I advise slow charging overnight whenever possible, monitor batteries at the field with ESV (or built in meters for TX), field charge if needed.