My bunny wants to be outside

New bunny owner. My son bought me Safari for Christmas from flea market. I love him so much but expenses at this time prevent me from going to Vet.
I am guessing he is a baby. Netherland Dwarf.
I Had to change work schedule to spend time with him at night. No problem. Self employed.
I know he needs neutering , although he was easy to house train except for my bed.
I keep plastic on till I can afford Vet, playpen etc. Soon!!
He is free roaming with open door cage ( the one he arrived in.
I feed him salad in morning and pellets at night. He won't eat hay anymore but I plan to use different types from suppliers instead of pet store. I may have spoiled him with fresh herbs.
I live in the city.
Lots of construction going on all four sides.
Animals. .... Possums.. Rats. Cats... Dogs..all looking for shelter because of massive construction and my huge community garden next door.
Lately Safari has tried to escape by scratching at walls in the foyer and jumping into Windows.
I keep going back and forth in my mind about the fact that he is a rabbit and may want to be free
I am such an outdoor person, and can not wait to take him to the garden come spring. Once he allows me to pick him up I have a harness waiting.
Clover, herbs, roses dandelion EVERYWHERE!
If he ever escaped, he would either be prey... (Owls got the garden cats baby kitten) or hit by a car.. Lots of speeding traffic.
I am so stressed because I feel so afraid but he wants outside desperately. Any advice would be so helpful.

You can set up a play pen in your yard, so you can use a travel cage to move him. So you can also sit in the run while spending time with him.

So can he enjoy a bit of time playing outdoors ^^

Taking him for a walk would be best! I do it with my rabbit all the time. Just remember that the rabbit walks you, and if you pull when he is facing you it can slip off (it has happened to us several times). The main reason you have the leash and harness it to keep him from getting into danger, not to lead him around. My rabbit loves running underneath the blueberry bushes, and he always drags me with him. Another option would be to use a playpen as @Hermelin said. You can find some for really cheap at yard/garage sales.
Could you send some pictures of him? We might be able to help with the breed if you answer some questions.

I would not interpret his jumping at windows as an attempt to "be outside" but simply exploring his surroundings and not understanding that glass is blocking him. If he's hormonal, any behavior can be inexplicable. If he were actually placed outside, he might be terrified for all we know.

Knowing his age would be most helpful. Maybe a local rescue could (for free) give you a general idea of his age. Age determines his diet too. If he's over 6 months, his pellets should be limited. Feeding too many can make him refuse his hay. Hay type also depends on his age.

As for taking him outdoors, I would suggest extreme caution. There are even more things to be aware of (and avoid) then you have already mentioned. Here is a run-down of things to consider before taking a rabbit outside. Once you've seen the cautions, I'd say the playpen is the way to go -- with constant supervision of course. Harnesses only work with rabbits willing to be harnessed. There are many unsafe harnesses out there and even the safe ones are not safe unless fitted properly by someone who knows what they're doing. Some rabbits can enjoy a harness, but don't count on it. Just consider it a bonus if he does.

In my experience rabbits who were born or raised outside and then become indoor pets often seem to want to get outside. I can't blame them, Sunshine and fresh air are lovely. It would be nice if you can find a way to safely spend outside time with your rabbit.

If you have your own space, a large chain link dog enclosure is a good start for outdoor bunny time. I suggest the top be covered with secured chicken fencing and the bottom part of the fencing be covered with lengths of opaque plastic corrugated roofing panels. That blocks visibility and can save the bunny if a dog comes along and starts chasing him through the fencing which can cause panic or injury. Also put small gauge wire fencing around the door panel so bun can't escape and nothing can get in.

Unless you can also bury fencing to prevent bunny from digging out or critters from digging in, only allow bunny run time when you can be there with him, or at least make sure you check for burrows regularly. They can burrow quickly and if the grass grows long you may not notice it unless you make a point of doing a regular inspection.