Yes, it’s normal for blood to flow to your head when you are upside-down. This is not necessarily a bad thing, but if you find yourself getting dizzy then definitely reduce the length of time you spend upside down. Everyone is different and some people can take a long time to acclimate to inversions.
As for your hamstrings, be patient with them. The “going to war” mindset will likely do you more harm than good. As for how long to hold your stretches, reread part one, section 5 of SYB. I give some guidelines at the end of that section. For the most part, the longer you can hold your stretches, the more you will increase your flexibility.