I've had my series 1 rx8 for about a month now. So far it's only had 3 complications. 1. The check engine light will randomly turn on and off (it varies each time I turn my car on). I know this is a pretty big issue and I'll be attempting to fix it soon. 2. When below ~1300 rpm it struggles to accelerate. Especially after stopping, it'll just bog up and take ages to pick up speed. So far, the solution that has come up after exploring some forums is to check the ignition coils and potentially change them. 3. The hand brake isn't working. When I try engaging it it doesn't click at all and I stead just gets really stiff trying to pull it up. This is the one thing I'm lost on and haven't found anything about how to diagnose it

I own a 2008, 40th anniversary edition rx8 with an automatic transmission (I couldn't find a manual in my area)

 

The parking brake is cable activated. The cable pulls on tabs on the rear brakes that activate the caliper to push on the pads and squeeze the rotors.

It is common for the cables to become corroded and stuck.

If you take the cables off the rear calipers you can see if they move OK when you move the brake lever inside the car. If not you need a new cable setup.
if the cable and the handbrake moves normally you need to check that the rear calipers are moving. If you live in a high corrosion area they can get seized up as well. Worst case you need the cables and two rear calipers..

 

The check engine light should come with codes that will tell you what the problem is. Start there, you can get it scanned at any garage or buy a $15 bluetooth OBD dongle.

While replacing coils is recommended, diagnose properly before buying parts.

By the sound of it I would not drive this car so you don't do more damage until you figure the first 2 issues out.

Rx8help.com for more info.