It is very save to do push-ups all day long every day...I would suggest doing them as often as possible until you ship. When you wake up, again after you shower, again after you eat breakfast, again mid morning, again after lunch, again a few times in the afternoon and before and after dinner, again a few times during the evening and then some more right before bed. If you wake up in the middle of the night to use the restroom do some more push-ups. Shoot for 600 to 800 a day!
Then all of this again the next day and the next day until you ship. If you will do this you should be doing more then the minimum at one time by ship date.
I would also add sit-ups and flutter kicks with every set of push-ups.
Do some right now...and then some more. Continue with as many as you can after you drop to your knees...
Pay is on the 1st and 15th so you might get your first check on July 1st but for sure by July 15th.
I will let others answer your other questions.
Please do some push-ups and then some more and then some more!
I wish you the very best.