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Normally with Meld into Stone, you simply can the wall at the point that you touched, usually right next to you. To walk in there, you have to use your movement.

Normally with Meld into Stone, you simply can enter the wall at the point that you touched, usually right next to you. To walk in there, you have to use your movement.

1. Wall of fire: What's a 'solid surface' and what happens if it stops existing?
2. Wall of fire: What's a 'solid surface' and what happens if it stops existing?
3. It must be large enough to fully contain your body. A surface is 2D and cannot contain anything. The only sensible reading is that the stone must be large enough to fully contain your body. Since you meld with the stone, it must be made of stone.
4. The spell does not specifiy, so these flavor aspects are up to you and your DM.
5. It is highly unlikely that you can cast a spell from a scroll, as your body is fully surrounded by rock, so you cannot see anything, and you need to read a spell scroll to cast it. If you cannot see the scroll, you cannot read it. Maybe if you had some kind of X-ray vision. It is also not clear if you can move in general other than casting spells on your self. Spells only do what they say they do, and Meld into Stone only says you can cast spells on yourself and "You otherwise can't move.". So you would not be able to move to retrieve the scroll, or unroll it, to cast the spell if you do not already hold it open, too. [This one might be worth a separate question.]
6. Unlikely as "You otherwise can't move." which would preclude you from using any equipment. [This one might be worth a separate question.]
7. When is a spell cast? and At what point does a caster define the target of a spell?
8. "to leave the stone where you entered it" you entered it a point you can touch (or remote touched with your metamagic), not a point in space. That is where you leave it again. I'd say, if the stone somehow is moved, the point on the stone is also moved, and you leave it at that point whereever the stone then is. Also, if you interpret this as a point fixed in space, you'd leave at the space where you entered, but that would not make sense, as you and the stone are not there any more. (But on this one, doublecheck with your DM. [It also might be worth a separate question.]).
9. Yes, but casting it at a distance might make it worse, not better, as it is easier to intercept you and stop you from entering the stone. Instead you could move to the wall, cast, and move in, with less risk and no wasted metamagic.

1. Wall of fire: What's a 'solid surface' and what happens if it stops existing?
2. Wall of fire: What's a 'solid surface' and what happens if it stops existing?
3. It must be large enough to fully contain your body. A surface is 2D and cannot contain anything. The only sensible reading is that the stone must be large enough to fully contain your body. Since you meld with the stone, it must be made of stone.
4. The spell does not specifiy, so these flavor aspects are up to you and your DM.
5. It is highly unlikely that you can cast a spell from a scroll, as your body is fully surrounded by rock, so you cannot see anything, and you need to read a spell scroll to cast it. If you cannot see the scroll, you cannot read it. Maybe if you had some kind of X-ray vision. It is also not clear if you can move in general other than casting spells on your self. Spells only do what they say they do, and Meld into Stone only says you can cast spells on yourself and "You otherwise can't move.". So you would not be able to move to retrieve the scroll, or unroll it, to cast the spell if you do not already hold it open, too. [This one might be worth a separate question.]
6. Unlikely as "You otherwise can't move." which would preclude you from using any equipment. [This one might be worth a separate question.]
7. When is a spell cast? and At what point does a caster define the target of a spell?
8. "to leave the stone where you entered it" you entered it a point you can touch (or remote touched with your metamagic), not a point in space. That is where you leave it again. I'd say, if the stone somehow is moved, the point on the stone is also moved, and you leave it at that point whereever the stone then is. Also, if you interpret this as a point fixed in space, you'd leave at the space where you entered, but that would not make sense, as you and the stone are not there any more. (But on this one, doublecheck with your DM. [It also might be worth a separate question.]).
9. Yes, Distant Spell and Meld into Stone can work together. Casting it at a distance however might make it worse, not better, as it is easier to intercept you and stop you from entering the stone. Instead you could move to the wall, cast, and move in, with less risk and no wasted metamagic.

Here, you simply can walk into the wall at the point that you touched. To walk in there, you have to use your movement, and that does not change.

All that changes is that you can pick a point up to 30 feet away as the point where you will be able to enter the wall. You still need to move to move to get there, and that means, you need to have enough movement for that If you pick a wall 20 feet away and you have 30 movement, no problem (unless someone stops you). If you pick a wall 30 feet away, you either need 35 movement or more, like a wood elf, or you need to dash, or have some other way to shortcut the distance.

Normally with Meld into Stone, you simply can the wall at the point that you touched, usually right next to you. To walk in there, you have to use your movement.

All that changes with Distant Spell is that you now can pick a point up to 30 feet away as the point where you will be able to enter the wall. You still need to move to get there, and that means, you need to have enough movement for that. If you pick a wall 20 feet away and you have 30 movement, no problem (unless someone stops you). If you pick a wall 30 feet away, you either need 35 movement or more, like a wood elf, or you need to dash, or move again next round, or have some other way to shortcut the distance.