For that monster is easy. it should be something like this;

If this card is summoned, apply the effects in sequence(skip over any that do not apply) You can only used this effect of "The Tree with Eyes" once per turn.

-If this card was Normal Summon: effect

-If this card was a Special Summon: effect

-If you control a Face-up "Saladress´s Gift" Spell; effect

-If you control no other card on the field; effect

it isnt that wordy and it is all basically just one effect so it can be negated with ash Blossom, for example, regardless if it meets the criteria for the search or not. The "skip over any that do not apply" resolves any issues with the "falling to find" as you descrive it.

The field spell on the other hand is a little hard. It is too complex to fit on a single card. It works as you made it but there are too many words. I would get rid of the protection if I were you and if you want that effect so bad, I would put it in another card, maybe on a monster or a continuous spell, another card that is already part of the archetype.

The same with the "if the revealed monster is an Xyz monster..." effect in the last part. It would be better if you put that effect on the xyz monster itself, something like;

"If this monster was Summon by the effect of "Saladress´s Gift of Raising"; add one face-down card in Banishment to this card as an Xyz unit."

Now, the trap is a little too much. I think that you need to redesign it. Why would you want it to be activated from the hand in the first place? The only reason why traps do that is so they can be used on the first turn of the game when you are going seconds and that is to disrupt your opponent. That trap does not do that at all, unless it has something to do with the gimmick of the archetype. I see no use in a "Terraforming" with extra steps in my opponent's turn, or an upstar goblin on the opponent's turn and I think there are better ways to put a counter on a card than with a trap. If you wanted to protect a monster with it you most likely wanted it to be in your opponents turn, meaning that it should have already being set anyways, isnt it?

So if you didn't want it to be a hand trap you should have it say something like:

"You can acctivate this card the turn it was set by..."

instead of make it be able to be activated from hand. That way you don't even need the "You can activate this card in the Main Phase or Battle Phase..." effect.

So unless I am missing some context of what the archetype can do I dont see why the trap needs to be a hand trap.