The noise could be coming from the harmonic balancer on the crankshaft. Remove the belt and start the engine. If the noise gets better the balancer is likely to be what is causing the noise. Also, look at the front of the balancer and see if the you see cracks in the rubber as shown in the photo below. The balancer is made in two parts with the rubber separating them. When the rubber goes bad it allows the metal parts to bang together creating noise.
Welcome to the forum Larry. sounds like you have taken on a good project. Your 1990 transmission isn't electrically shifted. There isn't a limp mode and there are no solenoids to replace. You transmission is hydraulically shifted with pressure changes in the valve body. Feel free to ask any questions about your Reatta that you might have.
Hard to answer that question accurately without more detail, top of which would be mileage and a bit of car history. The car looks okay overall, a nice driver based on overall appearance. A little grungy under the hood. It doesn’t need to shine but it doesn’t help the otherwise neat appearance
The key lock mechanism where you put the key only actuates the ignition switch at the bottom of the steering column. You can see the location of the switch in the photo below.