This is technically correct, but `anguillis` generally should be in the genitive case "anguillarum" for classical Latin - that is, "full 'of' eels", instead of the ablative which is used here, "full 'by means of/with respect to' eels".
> Navis volitans mihi anguillis plena est
The same criticism for `anguillis` applies here. Also, the usage of the dative of possession (mihi) is non-standard because it is usually reserved when you want to emphasize that a person has possession: "nomen mihi est Bob" -- "my name is Bob". The fact that I have a hovercraft isn't really the focus of the sentence - the fact that it is full of eels is far more interesting. It's not technically wrong, but I don't think any Roman would translate this sentence this way.
My Latin is rusty but "navis aëricumbens" invokes the image of a ship driving through the air like a skiff through water. Much better than just "flying ship" which reminds me more of an airplane than a hovercraft.
When in doubt you can always look what words the modern Romance languages use. Most seem to have a word similar to French "aéroglisseur", air glider.
AFAIK plenus requires an ablative: like in “gratia plena” (full of grace), “pleni sunt coeli et terra gloria tua” (heavens and earth are full of your glory) etc...
Plenus can take an ablative (cf. Allen and Greenough, §409a) but it can also take an objective genitive (cf. §349a). I'm pretty sure the objective genitive is preferred (at least in poetry, according to A&G), but I could be wrong.
> Mea navis volitans anguillis plena est
This is technically correct, but `anguillis` generally should be in the genitive case "anguillarum" for classical Latin - that is, "full 'of' eels", instead of the ablative which is used here, "full 'by means of/with respect to' eels".
> Navis volitans mihi anguillis plena est
The same criticism for `anguillis` applies here. Also, the usage of the dative of possession (mihi) is non-standard because it is usually reserved when you want to emphasize that a person has possession: "nomen mihi est Bob" -- "my name is Bob". The fact that I have a hovercraft isn't really the focus of the sentence - the fact that it is full of eels is far more interesting. It's not technically wrong, but I don't think any Roman would translate this sentence this way.