I looked up the model number you posted and couldn't find any exact information.
It does look like you can run Windows 7 64-bit. There's no mention of Windows 8 compatibility, but that doesn't mean it won't run Windows 8 - it's more likely that the only reason it doesn't mention Windows 8 is because Windows 8 wasn't out when your computer came out.
What I could not find is the maximum RAM that the laptop will support. Note that even if the OS can support more RAM, laptops often/usually have physical limits to the amount of RAM you can put in them based on the motherboard and/or memory slots/bus.
If your computer uses DDR2 RAM it appears that 4GB is the maximum RAM it will support. If your computer uses DDR3 RAM it looks like it can take a maximum of 8GB RAM.
You can determine if you have DDR2 or DDR3 RAM by going to Control Panel >> System and looking at the memory information.
HP Pavillion DV7T-3300 Laptop | i7 Q720 @ 1.6 GHz | 4GB RAM | Win7 Pro 64-bit
m-audio Axiom Pro 61 keyboard controller || iPad2 | RetouchControl DUO | TouchOSC | LoopBe30 MIDI
m-audio Mobile Pre USB (original) audio interface | ASIO4ALL || RØDE NT-3 mic
Reason 6.5.3 || Pulsar | Saturation Knob | Rough Rider | TSAR-1 | Uhbik-A | Re-Tron | Polar | Echobode | Uhbik Q | Uhbik F | Morfin XF | Uhbik S | Uhbik D | Uhbik G | CV Suite Line Processor | wbl5515 | Uhbik P | RE-2A | Radical Piano