Yes, you can.
As stated in the spell Gaseous Form:
The creature is subject to the effects of wind, and it can’t enter water or other liquid.
Emphasis Mine, size doesn't matter in a gaseous form, as you will be subject to the effects of wind as any other gas would be
In addition to the effects noted, a gust of wind can do anything that a sudden blast of wind would be expected to do. It can create a stinging spray of sand or dust, fan a large fire, overturn delicate awnings or hangings, heel over a small boat, and blow gases or vapors to the edge of its range.
With Rules as Written, you can definitely cast Gust of Wind as a standard action, then using your move action to move into the gust, to carry you along.
If I was GM though, I would rule against this use, as the spell to me seems intended that a single blast of wind comes from the caster, moving away. The actual ability of the caster to get caught in the gust seems very ambiguous. It's your game though, and if you feel that the Vampire would be best served as a storyline villain, and not just a once off, that's something to discuss with the table. Just make sure you don't have anyone ready to snipe him off after the 60 ft. that he moves.
There are no rules for this, so it's always going to be up to the DM.
Polymorph can be used on "a creature you can see", with no further restrictions. It (for all intents and purposes) automatically fails against shapechangers and creatures with 0 hit points, but that's as far as it specifies. There's one clause in Polymorph which could be argued to apply here:
The
target’s
gear
melds
into
the
new
form.
The
creature
can’t
activate,
use,
wield,
or
otherwise
benefit
from
any
of
its
equipment.
So if your DM considers a swallowed creature to be "gear" (unlikely), it would meld into the new form. Otherwise, Polymorph has no rules for this situation.
As you've noted, the rules within each creature's statblock have nothing that covers this situation either. It's noteworthy that, while each of them can only swallow creatures of a certain size, there's nothing that says what happens if a creature they've swallowed grows beyond that size. So, as a DM, I could certainly see an argument that when a creature you've swallowed becomes too big for you, the swallow ends messily.
Another point to consider about the rules for swallow within each creature's statblock are just that - within each creature's statblock. There are no global rules for swallow. Well, so, what?
The
target’s
game
statistics,
including
mental
ability
scores,
are
replaced
by
the
statistics
of
the
chosen
beast.
This means that, once Polymorph is cast, the rules that allowed the creature to have another creature inside it have ceased to apply to that creature. What does that mean? The only sensible way to deal with this paradox is to accept that the rules just don't cover this and the DM is going to have to decide what happens.
Best Answer
D&D 5e just isn't this simulationist
The question can't be answered by the published D&D rules, as the game is not meant to simulate such interactions in any way 'realistically'. The intent of Gaseous Form is to give various advantages of movement and protection to the user, and though there are limitations it is not meant to be accidentally deadly. Weather in D&D is often used to provide atmosphere, and what small space is given to mechanical details in the DMG does not cover this kind of hypothetical situation.
Gaseous Form
The spell description gives all the benefits and limitations expressed by the rules, and it says nothing about rain. Though the description says:
the intention of this is to allow the beneficiary to move like a gas, giving some benefits, but be stopped by solid bodies of liquids, like the surfaces of rivers, lakes, seas etc.
Rain in D&D
As a DM, I use weather mainly to provide atmosphere, and this approach is supported by some advice to DMs in the Starter Set:
Of course, the fact that the DM has described it is lightly raining can, at the DM's discretion have some mechanical implications (e.g. walls are slippery and so the DC is higher to climb them). But the only generally-applicable mechanical information about rain that I am aware of is in the DMG, p. 110:
Note that this is only describing an extreme weather condition (heavy rain, not any rain), and in any case no mention is made of magical effects like gaseous form.