Do Car rental companies hold cars? I m seeing online that if I rent it a week earlier, its much cheaper?

No, they don't "hold" cars. If a car is sitting in their lot it isn't generating any revenue. You can reserve a vehicle in advance, no problem.

Some rental companies offer weekend specials with limited miles from friday to monday morning. It cost me $45 to rent a car from friday morning to monday morning. Any other day of the week its $30 per day. If i had rented it from thursday to monday would have cost me $75. Shop around.

They may allow you to schedule a rental...but I don't think they can guarantee the same exact vehicle will be available.

No. The reason the price is so high is that there is greater demand next week when many people start taking holiday trips. You could "reserve" a car for next week a year in advance but it would still cost the same amount.

The exact vehicle might not be there but something it its class will be; for instance you might rent a Jeep but get a Toyota RAV4

No. Your rental cost will be based on the specific dates you have the vehicle in your possession. You can certainly prepay for any time period but you can't base that rate on dates which you are not actually renting.

I really doubt it. So many things REALLY go up, if they fall closer to a holiday, for example, airline tickets too. But you can certainly ask - no harm in asking...