Madrid Airport Terminal 2 to Terminal 1 Connection

According to the Madrid-Barajas Website you may transfer:

From terminal T1 to terminals T2 - T3 through a free bus service connecting baggage claim hall 1 and baggage claim hall 2 in terminal T1, and baggage claim hall 6 in terminal T2. This connection can be done walking and you must go through security checkpoints, and takes around 10 minutes.

(Disclaimer: I have translated this myself from spanish to english as their translation was terrible).

Also here is the bus schedule and approximate times between Terminals:

(This image is straight off the website linked in english. SEE told you it was terrible.)

At the end of the day, one will likely have to exit the secure area, transfer over to T1 and pass through security and passport controls once more. At least from the info posted on the airport's website...

Which airline are you flying on? Can you check in all the way to JFK? If you're using a different carrier for the second flight, they might require a document check to make sure you have an ESTA or US visa. In that case, you might need to go to a check-in desk.

If you're checked in for both flights and there are no delays, 1.5 hrs sounds doable. If you're on one ticket, personally, I think it should be possible. If you booked two separate tickets I'd consider the connection somewhat risky (mostly because of a potential delay of the first flight).

By the way, this has been discussed before: Connecting in Adolfo Suarez Madrid-Barajas airport to travel to the UK and Changing terminals in Madrid airport

There is a train connecting the baggage claim areas of both terminals.

There's also a post on Tripadvisor. It sounds like you would need to go through security again.

You will can take the bus or you can walk.

Just follow the signs to the terminal shuttle bus, which is free, and hop on. The buses leave every 5 minutes. It's about 10 minute trip give or take.

On foot 7 minutes minimum depends from what gate you are coming from and what gate you are going to which you don't know now.

You will have to clear security AND immigration at T1. One hour thirty minutes means if there are any delays of your arriving flight, you're very going to miss your flight. Don't forget that this is an international flight, you must get to check in counter at least about 45 minutes before your flight.

You're cutting it close. If you haven't purchased your ticket yet or you can change it without cost, I'll advise you change it to allow yourself time. Tickets from Barcelona to Madrid are very cheap if you even have to buy a new one altogether.

Good Luck!