For trains that have reserved seats, likely only the first car is. You can always get on any train, and there will be non-reserved seats.
Tel Aviv - Haifa is a great route, a lot of it on the water, very pretty, and reasonably quick. Definitely better than the bus. I believe it's shorter, but also more comfortable. You have a wider aisle, and every 2 seats face 2 seats, and you have more legroom, outlets, bathrooms... A no-brainer. And there's no problem bringing a carry-on or a piece of luggage. I've seen people (such as myself one time) take even 3 pieces of luggage without a problem.
For Tel Aviv-Jerusalem, go with the bus. If you're looking to get to Haifa, take the 480 to Arlozorov, and take the train from there. It's the quickest bus to Tel Aviv, and from there, you're right by the train. The only reason I'd suggest taking the train is if you're traveling in 2017 when the high speed train between the 2 is (supposedly going to be) finished.