Firstly, when you’re a temp, you’re a temp and any benefits you get from that are from the temp company only.
When you are full time with Company X, you are full time with Company X and any benefits you get from that are from Company X - the two have nothing to do with each other.
Secondly, having a 6 month waiting period for certain benefits to kick in is pretty normal. At the company I work at (a University) there is a 6 month waiting period for certain benefits to kick in (dental coverage, tuition support, etc). At all of the companies my husband has worked at (electrical) he’s had to work a certain number of hours before benefits kick in. This is very common.
Thirdly, you need to look at your contract and determine what your rate of pay is for what number of hours. It’s also very normal for a temp employee to work hours per day of X, with full time salaried employees working hours per day of Y. That doesn’t mean that the full time employees are are working overtime - it means that’s how long their work week is. Depending on your location and contract you could be working 9 hours a day with a 30 minute lunch break and not be considered as working overtime. Conversely, my regular (full time employee) work day is 7 hours whereas temps at my company typically work 8 hours and do not receive OT.
Fourthly, I’m not sure why your PTO would be prorated from 11 days down to 2. If you’ve worked 1/2 a year at the time you want days off, I would think you would have about 5 to use - not 2 (although, again, this depends on your contract).
Finally, getting ANY paid time off at Christmas is really a luxury - not a typical entitlement. Also, as a newby, will you even be allowed to take days at that time of year? Unless your business closes over X-mas, I would expect that long term employees would get to take that time off first if they choose, with newbies such as yourself having to work. That would be pretty standard procedure, I think. Again, my husband can take time off whenever he wants (well, if it’s at the end of a job he’s not going to make any friends) but he doesn’t get paid for it. Even if it’s at X-mas time.
Sadly, these are the realities of working a full time job - you get what you get, you’re entitled to what you’re entitled to and your employer is NOT going to put your needs first. You need to choose a position with all of this in mind and make sure that what you sign up for is actually something you can live with. For instance, in the private sector I could be paid a lot more $$ than I do working at a pubic university; however, I would have longer work hours, less vacation time, no tuition benefit, etc. There are choices to be made and you need to decide which choices work best for you.
FWIW, it is now August - if you need to take time off at X-mas to be with your family and you’re confident that you will be able to get that time off from work, you need to start budgeting and setting aside $$ NOW to cover the period you will not be paid for. Assume you make $100 a day and you want to take 5 days off at X-mas - set aside $5 per day ($25 per week) and you’ll have your $500 waiting for you in December.