Underlaget er tyndt, men jeg sover godt i soveposen alligevel.

Because underlaget is a neuter singular noun in Danish.

Adjectives in Danish often agree with the noun:

• common gender singular: tynd
• neuter singular: tyndt
• plural/definite: tynde

So:

• en tynd madras
• et tyndt underlag

Since underlag is neuter, the predicate adjective after er becomes tyndt.

Underlaget is the definite form: the mat/pad/base/layer.

In Danish, definiteness is usually added to the end of the noun:

• et underlag = a mat / a pad / a base layer
• underlaget = the mat / the pad

So instead of using a separate word like the, Danish often uses a suffix.

It is a fairly broad word. It can mean something like:

• surface
• base
• mat
• pad
• groundsheet
• sleeping pad

In this sentence, it probably refers to the thing the speaker is lying on while sleeping, so in natural English it might be something like sleeping mat or pad rather than just surface.

Because sover is the present tense form of the verb at sove.

Danish verbs do not change much, but they do have a present tense ending:

• infinitive: at sove = to sleep
• present: sover = sleep / am sleeping

So:

• jeg sover = I sleep / I am sleeping

Using jeg sove would be grammatically wrong.

Here godt is being used as an adverb, not as an adjective.

Compare:

• adjective: en god pose = a good bag
• adverb: jeg sover godt = I sleep well

In Danish, many adverbs are formed with -t:

• god → godt
• hurtig → hurtigt

So sover godt means sleep well, not sleep good.

They do related jobs, but they are not the same.

• men = but
• alligevel = anyway / nevertheless / even so / still

So the structure is roughly:

The pad is thin, but I sleep well in the sleeping bag anyway.

Here:

• men connects the two clauses
• alligevel adds the idea of despite that

Using both together is completely natural. It emphasizes contrast.

That is a very natural position for it in Danish.

Alligevel is quite flexible, and its placement can vary depending on emphasis. In this sentence, putting it at the end sounds natural and gives a nice final despite that feeling.

You could also see it in other positions, for example:

• ... men jeg sover alligevel godt i soveposen.
• ... men jeg sover godt i soveposen alligevel.

Both are possible, though the exact rhythm and emphasis change a little.

Soveposen means the sleeping bag, while en sovepose means a sleeping bag.

Danish often uses the definite form when the object is already understood from the situation. If the speaker is talking about the sleeping bag they are using, i soveposen is very natural.

So:

• i en sovepose = in a sleeping bag
• i soveposen = in the sleeping bag

Both can be correct, but they mean slightly different things.

Because Underlaget er tyndt is the normal way to say The pad/mat is thin.

It follows a very common Danish pattern:

subject + verb + complement

• Underlaget = subject
• er = verb
• tyndt = complement

Det er tyndt underlag would not express the same idea naturally. It sounds more like That is thin material/base and is not the normal way to describe this specific item.

Usually sleep well is the most direct match.

But depending on context, it can also imply:

• sleeping comfortably
• sleeping soundly
• having no problem sleeping

So in this sentence, even if the surface is thin, the speaker is saying they still sleep fine in the sleeping bag.

Yes, but it follows normal Danish rules.

After men, you start a new main clause, and Danish main clauses normally have the finite verb in second position:

• men = linker, not counted as part of the clause itself
• jeg = first element of the clause
• sover = second-position verb

So:

• men jeg sover godt ... is correct

If you moved another element to the front, the verb would still need to stay in second position:

• men i soveposen sover jeg godt alligevel

That is also grammatical, but it gives different emphasis.

Yes, it sounds natural.

It is simple, idiomatic Danish:

• Underlaget er tyndt is a normal descriptive statement.
• jeg sover godt is a very common expression.
• alligevel is a common word for anyway / nevertheless.

It sounds like something someone might say while talking about camping, hiking, or sleeping outdoors.