Ah, fun one! First off, and this may blow your mind in a fun way (it did mine): DD v4 doesn't (to my knowledge) specify how and when Hit Dice are thrown to determine HP. For me, it doesn't make sense to treat it like later rulesets where you are adding the HD for a new level to the currently existing total for the previous level. Instead, at each level, throw the new HD, and take the higher value of the thrown total, or the character's current HP.
For example, 1st-level Fighters have 1+2HD, and Bev the Fighter throws 1d6 at 1st level (value: 4) and adds 2 for a total of 6 hp.
Level 2 Fighters have 2+1HD. Upon gaining level 2, Bev throws 2d6 (3+6) and adds 1 for a total of 10. That is higher than the previous value, so 10 hp it is!
At 3rd level, Bev throws 3d6 and has bad luck, 2+1+3 = 6. So max HP stays at 10 and there is no HP gain from level 3.
This is very different from later rulesets, as I said, and can take a bit of getting used to! But I find it very refreshing, and in my campaign I've taken it further: HD are rerolled every time you get a rest in town, and you keep the higher value of the total thrown, or current HP (after any damage taken while adventuring). In this way it doubles as a healing mechanic.
If you're curious, this way of determining HP is made explicit in M. A. R. Barker's Empire of the Petal Throne
(as published in 1975 by TSR), which was one of the 1st "hacks" of the original D&D rules.
Now for the elf: I know that there are several ways elf levelling has been run in the play-by-post games here, all of which are fair interpretations. Here's how I would run them by-the-book (DD v4):
- At 1st level, elfs choose a class. They obey all the rules for that class. After the adventure, any XP earned is assigned to that class.
- In between adventures (in my campaign this is any time the elf is in a town for a night or more), the elf may switch classes if desired.
- Once the switch happens the 1st time, the elf can use all the benefits of both classes simultaneously when adventuring, but XP per adventure is still assigned to one or the other of the classes.
- When an elf gains a level in one class or the other, they roll the new HD for that class level, and if the total is higher than their current max HP, they take the new value.
- For to-hit & saves they use the more favourable value.
For example, Sir Elf the Elf starts out as a Fighter and rolls 1+2HD for a total of 5 hp. He wins some treasure, and returns to town. The next time he goes to the dungeon, he decides to adventure as a magic-user. He rolls the 1st level magic-user HD (1) at this time, and gets lucky with a 6! He now has 6 hp. He can use any weapon, but he can only cast spells if he takes off his armour.
He adventures once as a MU, but then mostly adventures as Fighter, and after a few delves he gains 2nd level as a fighter. He rolls 2+1 HD, and gets an 11!
The next level he gains is Fighter 3rd, and he rolls 3 HD, but he has horrible luck and gets a 3. His hp remain at 11.
For your F4/MU7 elf, you could do several things: just roll the "last" HD for each class (4HD and 5HD, respectively), and take the higher. But more fair to you would be to roll each level, starting with e.g. 1st level MU at 1HD, then 1st level Fighter at 1+2 HD, then 2nd-level MU at 1+1 HD, etc up the charts. Each time you roll, take the new total only if it's higher than the previous.
Hope that all makes sense! Again, this is how I run it, and I know different refs have other methods.