1) If I buy weapons before equiping the drop ship, no weapons are available to equip my soldiers.
Yes, this is a known bug. Only the first 8 can be equiped. If you select and equip soldiers further down the list, they will enter combat without weapons.
2) I can't seem to get the drop ship to the target...
I've had this issue as well, but it's hard to duplicate. I save before I send a ship, then, if it doesn't work, I can try again.
One method that seem to help me a bit was to retarget the ship to any point along the path, then after letting it fly a bit, retarget it to the downed ufo.