Merry Christmas! That's not a bad haul of presents you've got there at all, so let me see if I can help you along at bit.
So, at present (pun most definitely intended) you've got: 20 Spearmen, 20 Archers, 8 Silver Helms, a Chariot, a Phoenix and 2 Eagles.
Right, on with your questions:
1) I would always go for Spearmen and I would strongly advise you to do the same. However, as a fairly recent thread showed, a number of people would advise you to take Sea Guard instead. However, I think Spearmen are vastly superior. Whilst LSG do give you some extra shooting (including stand and shoot), the damage output they kick out (bearing in mind the fact that, as primarily a combat block, you'll want to be moving them around) is very minimal for the fairly steep points cost. A points cost that could be used to buy, say, a unit of Archers, whose shooting prowess is far more useful. Also, HE want to be spending as little as possible on Core, since, well, our other units are far better. As a general rule, aim for bang on that 25% limit. You already have a lot of core, so you don't want to be bumping that cost up by using LSG over Spearmen.
2) A Frost Phoenix is usually far superior. The exception comes is when you are using a full cavalry list, or any other list that struggles to deal with large block of infantry. Here, the Flamespyre is far more useful to your army, thanks to its ability to fly over stuff and burn it.
3) I would usually go for a Lion Chariot, purely because it can smash into stuff and cause a lot of damage. Horse chariots are indeed cheaper, and fairly useful when taken in groups, but chariots aren't that useful anyway, so, I'd just stick with a Lion Chariot.
4) Most of it comes back to the Core thing I mentioned. Although you will probably use everything - save perhaps the Griffon, which you could however use as another Eagle - you will have a lot of redundancy. That is, if you want a good list, you won't be using everything at once. That's not necessarily a bad thing, since it allows you to change up your list from time to time, but it is a question of cost in that would you prefer to spend less and just have one potential army list? If so, another box of Spearmen or Silver Helms will do you for Core, depending on your chosen list, and you can buy characters separately.
5) Well, obviously, none of your Core can fly but, aside from that, you can do quite a lot of flying. Phoenixes and Great Eagles are all fantastic units, whilst Skycutters and Eagle/Griffon mounted characters are usable as well. It's probably not the type of list you'd take to tournaments, but it's a fun thematic list that will be more than capable of winning games.
Finally, as for what to buy next, I'd definitely pick up another box of Spearmen, or at least acquire some in some way. 20 Spearmen on their own won't do much, but 36 is a good sized unit. Of course, you may be set on cavalry for your core, in which case you may want an extra box of silver helms. Next, I'd choose what Specials you want to include. Pretty much everything works, but a large unit of White Lions is probably the number one choice. Finally, pick up a couple of mages (one to be an archmage) and a Noble
BSB and you should have a good list. Let me know what you may want to include, or let me know if you want anymore advice and we should be able to make a good shopping list for you
Hope this helps!