So IMO, when you're not casting on yourself, you can only use spells that work without line of effect (like clairvoyance or nightmare).
OK - So we agree you can cast personal, touch or other ranged spells - so long as the "target" is "you" or other object on your possession or "point in space" near you - but not "out of" the melded area (eg. the solid piece of stone where you reside);
For Example:
1. Bulls Strength cast on you by you will work; Range: Touch;
2. Lightning Bolt will _not_ work unless cast on you; Line of effect past you does not exist; And stone "reflects" the LB (?)
3. Chaos Hammer a "multicolored explosion of leaping, ricocheting energy"/burst (or Circle of Death), does *not* affect others (other than you) because the "line of effect" is broken (similar to a fireball not going through unbroken walls);
4. Death Ward would work - if cast on you (Range: touch);
5. Dimension Door or Teleport would work - on you only;
6. Ethereal Jaunt would work - but would immediately end your "meld with stone" spell as would any other similar (ie. blink) spell
7. Forbiddence or certain scrying spells which require "sprinkling" material components or extended use of large amounts of material components (or "creation effects" such as Heroes Feast) would not work (good catch!);
8. Minor or Major 'Globe would work (and "shunt" you out of the stone - 5d6 damage - ouch)
9. "Cloud" Spells or other "spreads/emanations" would not work (while the "center" was in the stone);
10. Assuming you can "see" creatures through "clairvoyance" or similar, you cannot cast "at" them due to "line of effect" limitations for most spells; see below (incl. magic missile or phantasmal killer);
11. Spirtual Weapon could be cast but not "directed" until you are our of the stone
12. Summon spells would not work due to "line of effect" - see below
13. Symbol spells could only be scribed onto surface in your possession;
PHB p.176
Line of Effect: A line of effect is a straight, unblocked path that
indicates what a spell can affect. A line of effect is canceled by a solid
barrier. It’s like line of sight for ranged weapons, except that it’s not
blocked by fog, darkness, and other factors that limit normal sight.
You must have a clear line of effect to any target that you cast a
spell on or to any space in which you wish to create an effect (such
as conjuring a monster). You must have a clear line of effect to the
point of origin of any spell you cast, such as the center of a fireball. A
burst, cone, cylinder, or emanation spell affects only an area,
creatures, or objects to which it has line of effect from its origin (a
spherical burst’s center point, a cone-shaped burst’s starting point, a
cylinder’s circle, or an emanation’s point of origin).
An otherwise solid barrier with a hole of at least 1 square foot
through it does not block a spell’s line of effect. Such an opening
means that the 5-foot length of wall containing the hole is no longer
considered a barrier for purposes of a spell’s line of effect.