Congratulations on your purchase. Post some pictures and show off your ride!
I have an MKII, but I'll try to address your questions to the best of my knowledge:
1. Unless you live outside of CA, you should probably get an exhaust.
2. Here is a link to your speedometer question:
MR2 Technical Knowledgebase - MK I Speedometer cable 101
3. Here is a link to your electrical issues:
MR2 Technical Knowledgebase - Electrical Problems 101
4. Regarding your windows. Its probably a window regulator or power window gear (check out Twosrus.com for a replacement to the OEM). Good thing its not a motor.
5. The lights in the gauge cluster could be an electrical issue or just a faulty dimmer switch. Change out the dimmer switch first and take out the gauge cluster and wiggle the connections in the back if the dimmer switch isn't the culprit. While its out, you can change out the bulbs to leds (look up board member BEN for help on this)
If you need some OEM replacement parts, contact Aaron Willis at Lithia Toyota (awillis@lithia.com). He has an MK1 as well and is very knowledgeable. Since he is a board sponsor, he gives us great discounts on new OEM parts. Congrats again and welcome to the board!