Can you attack bases with jets/missiles/nukes? Land bases? Air bases? Sea bases?
Yes.
Do attacks on air bases cause collateral damage to any grounded air units?
An air attack on a sector (regardless of what the target was when the air attack was set) will attack everything within the sector. For example, setting an attack on a sector means the attack should go to that sector, and setting an attack on a land unit means the attack should do to whatever sector the land unit is in when the attack happens. However, in either case, the air attack will damage anything in the sector it's attacking.
Also, I noticed it said bases start with a strength of 1000. What do this imply? its "lifepoints?" Do it go down?
It's the base's "health," basically. It's also directly comparable to the strength of units. For example, a missile has an attack power of 300, so it would take 4 missiles (disregarding any random factors and such) to destroy a base. Sending two missiles would take away more than half of the base's strength.