Dinnercoat

So I went to go look at this 87 GXL, it only has about 78K miles, stock everything with the paint being in good shape aside from a minor scrape here and there, inteior is good too. Checked out the engine, little smoke on the first start up but that was expected, let her warm up then revved it to 4Krpm for about 15 seconds and no smoke.

Took it for a test drive and drove well, clutch was about as worn as was expected to be, pushed down on the rear end of the car and was nice and stiff and the price was right so I got it.

I went with my girlfriends step-dad and on the drive home as I'm behind him my horn and caution lights just start going off like crazy so it looks like the alarm is messed up. Whats about the easiest way to disable the alarm for the time being before I can get a chance to find the source of the problem and fix that? I was hoping to take the car up to my dad's tomorrow for a dinner thing he's doing.

Also it was weird like right after I bought it and was driving out of the city with the car I noticed the rear-end would shudder as I came out of a dead-stop into 1st. It doesn't exhibit this behaviour when shifting down or up into any other gears, only 1st from a stop. Any thoughts on that too would be great.

Once I'm sure I can drive around without my horn blaring at everyone and caution lights flashing I'm planning on taking it to a Mazda dealership to run a full diagnostic on it so at least I can see what things will need to be down the road as well as what needs to be addressed now.

Thanks!
(I'm also running vin checks for people with the carfax account I made to check the vin on this car so if you need a vin checked I have a post in the vin check thread)