In most countries, including the US and in Europe, it is illegal to operate any self-built RF transmitter without a license. That includes the ISM band. ISM transmitters are exempt from the need for an operating license, but building transmitters for this free band is still restricted. The builder or manufacturer needs to certify that the device indeed respects ISM specifications.
Someone with a Radio Amateur license may build and operate RF transmitters under certain restrictions.
The Radio Amateur license might cover radar experiments at least in some countries, see this question on StackExchange for Amateur Radio: https://ham.stackexchange.com/questions/14650/can-i-use-a-amateur-license-to-experiment-with-radar.
Universities and companies that do research on or development of radar, and need to test radar equipment in the field, require some sort of license for their organization.
In any case, your question seems to be about operating existing radar units, rather than building one yourself. The situation should be somewhat similar for aviation and marine radar. If you buy a (legal) aviation (or marine) radar unit, this device will be certified, and allowed to be operated by a certified user. That user will require a pilot license (for planes, or radio license for boats). The device certification only covers operation in the intended environment, that is built into the plane (or the boat), but does not cover land based operation, away from the plane (or boat). You may find discussions about that in the internet (like https://www.reddit.com/r/amateurradio/comments/7zu3x5/does_anyone_have_experience_operating_a_marine/).