Okay those were, imho, some pretty good ideas, and they made me think too.
alright, cause i'm lazy, i dunno if anyone specifically stated this:
the world map for all 16 levels would not work since randomization of each individual level.
however, if you make an area as a world, it should work just fine.
Remember, he's splitting the 4 areas into 4 worlds and probably using custom levels or semi-random levels as the bulk of a world. (Is that right?)
2. ability to keep collected items however, you can only use so many at a time (not including: bombs and ropes and other items snagged in that run) so like, 2 specific carryover (also, udjat eye/spectacles/etc are not included in total) items like a jetpack, pick axe, etc.
I like this, but perhaps only one item per "slot", similar to TLS.
Example: Weapon slot holds guns, knives and bows; Body slot holds Capes, Jetpacks, Compass and so on; Shoe slot hold shoes etc.
Then maybe you can buy these items (for a big price!) in the overworld, and you lose them when you die, OR obtain them normally as in Spelunky (possibly keeping them for the next level you play if you win?)
3. shortcuts to places of specialness if unlocked.
4. if you run out of lives, you must start ALL OVER.
I pretty much agree with this entirely.
5. *possibly* make each area just a bunch of levels straight through, without the score screen, however, if damsel/idol reach the bottom, it will just automatically be added to the total. also, when you run out of hit points, and die, you only start the section over, not the whole area.
Yeah, this sounds all right. Maybe having a 1-up sort of item could help, too, since this game is going to include potentially difficult CUSTOM LEVELS!

7. quick save option, so you can start up again fromt hat save file once, but it's there for if you really have to go do something, and it may take hours.
This. Exactly.
8. ability to save the map after completing the whole game. and be able to start a new one without deleting the other world.
Beat the game --> Never game over or have continues --> I like it. Easy to replay the highlights.
9. carryover money (if not mentioned before) as well as squares where you can go directly to a shopkeeper and buy/gamble/havesex.
You mean an overworld shop? Great, as long as it's expensive and/or limited in stock. We can't have an overworld shop being as good as any underground!
EDIt:11.? make save file part of the game itself so if you transfer it onto a flashdrive your data will remain unchanged even when played on a different computer if possible.
I don't know about that. If it's just a quicksave, that is, the kind of save that's valid for only one use, why let people copy it? It's kind of asking to be exploited.
Anyway that's my 10 cents. Sorry about the wall.