Windsor Castle: Absolute MINIMUM connection time

Probably 6 hours at an absolute minimum. Plan on

1.5 to get out of customs and to the taxi rank.

.5 Taxi to castle

2.0 Tour castle (just the bare minimum though)

.5 Taxi back to airport

1.5 Check in, security, get to gate.

Really, if you have less than 2 hours in Windsor, it is not worth the expense and headache from Heathrow. Same for getting into London proper.

If you don't have the time, consider renting a hotel to freshen up in and relax, or just stay at the airport.

Windsor Castle doesn't open until 09:45 so if you have a red eye it mmay affect your schedule.

Most people take about 90-120 minutes to go around the castle (you get an audio tour device with admission). The coach tours allow about 2 hours or a little over and its a 10-15 minute walk to/from the coach park.

At Heathrow if you have luggage checked through on your next flight then about 40 minutes if you have a non EU passport, but its a bit of a lottery depending on the flights arrived in front of you and where they were from.
If you have boarding passes for your onward flight it may take anything from 5 to 20 minutes to go through security/customs again.

You would really need to prebook a taxi, a cab from the rank won't do. A Windsor taxi should charge about 50 GBP return and the journey is about 20 minutes each way.
There are also several public buses an hour from in front of Terminal 5 that take about 45 minutes and are much cheaper, they go the scenic route and pass through Runnymede (Magna Carta)

you should consider an overnight if there is complex travel and custom involved. then you get to enjoy the town in the evening (walking along the wall under full moon is pretty impressive), and it's a short walk to eaton college (see kids dressed like harry potter walking the street is interesting), and have a beer at the bar where Williams and Harry used to hang out.