Hello windymary,
1) is is better to inflate in the beach, due the board is really light and if you take on the roof depend the distance and how windy is the air the board it may bend and can weak the new anti bend system than certain boards company used to keep the the more straigth while padding in the water.
Also if you roof rack have imperfection can pich or scratch your boar and you will not able to inflate.
I used to travel in the roof rack but was very short distance inside the city 5 to 10 min driving no problems.
2) the board are light and easy to carry
3) all come with bag but it depend the brand some have wheel for easy transportation
I used 3 part paddle so you can keep in the same bag while travel, the bags should have enough space for the basic, paddle-leash-wetsuit
4) Inflate is depend how fancy or fitness you want, the manually pump is easy but take 5 to 10 min but when you finish you already warn the upper body ..
Fancy way they sale a automatic electric pump which is portable is coming with a battery and the option to connect to your car battery using cables, for inflate, is take 2 min to fully inflate is really nice i had both system manually and automatic
the best is automatic jeje
4) normally leave in the car or you can leave on the beach
I used to travel with the INflatable board, domestic inside Mexico without problems. But once I travel to Ecuador a placed named Monta?itas and the people for security on the airport call me and retain for a 10 minutes..?
i take the automatic pump inside the travel bag, on the X ray machine, they saw a square box that the X ray machine can not see inside, due the battery body is lead they found suspicious, and was more fun when they ask what is this i .. ( in Spanish pump is Bomba in Spanish but in English is ...BOMB
And this word are forbidden in airport... and the end I had to take out the board and show how is working, lucky for me the battery was fully charge it's work and continued to travel...
My recommendation is check the bag functionality, the board is they have automatic or only manually, for sure the automatic pump is extra $$$.
i post some pictures on my board and the automatic pump
saludos