Пусть сливки и довольно густые, я иногда добавляю их в соус.

Not in this sentence.

Here пусть is part of the concessive pattern пусть ... и ..., which means something like:

• although
• even if
• granted that
• admittedly

So Пусть сливки и довольно густые, я иногда добавляю их в соус means roughly:

• Although the cream is fairly thick, I sometimes add it to the sauce.

This is different from the more familiar пусть meaning let or may in sentences like Пусть он войдёт = Let him come in.

In Russian, сливки is normally a plural-only noun (pluralia tantum). Russian treats cream as something that grammatically behaves like a plural noun.

So you say:

• сливки свежие = the cream is fresh
• густые сливки = thick cream

Because the noun is plural, any adjectives and past-tense verbs agreeing with it will also usually be plural.

This is just one of those vocabulary items you have to learn as a unit:

• сливки = cream, but grammatically plural

Because густые agrees with сливки, and сливки is plural.

Agreement in Russian means the adjective has to match the noun in:

• gender
• number
• case

Since сливки is plural nominative here, the adjective is also plural nominative:

• сливки → plural
• густые → plural

So:

• густые сливки = thick cream

Even though English uses singular cream, Russian still uses plural adjective forms with сливки.

Here довольно means:

• fairly
• rather
• quite

So довольно густые means fairly thick or quite thick.

A learner may know довольно as enough, but in this sentence it is an adverb of degree, modifying густые.

Compare:

• довольно густые сливки = fairly thick cream
• сливок довольно = there is enough cream

So the meaning depends on how it is used in the sentence.

Correct: this и is not a simple coordinating and.

In the pattern пусть ... и ..., the и helps strengthen the concessive meaning. It gives the sense of:

• even though
• admittedly
• granted that

So пусть сливки и довольно густые is closer to:

• Granted, the cream is fairly thick...
• Even though the cream is fairly thick...

You do not need to translate the и separately as and here. It is part of the whole construction.

Их refers back to сливки.

In я иногда добавляю их в соус:

• я = I
• иногда = sometimes
• добавляю = add
• их = them
• в соус = into the sauce

Since сливки is grammatically plural, the pronoun is also plural:

• сливки → их

Here их is the direct object of добавляю.

So literally the structure is:

• I sometimes add them into the sauce

Even though English would often say add it, Russian uses plural because сливки is plural.

Because Russian uses:

• в + accusative for motion into
• в + prepositional for location in

Here the idea is adding the cream into the sauce, so there is movement/change of destination. That is why we get:

• в соус = into the sauce

Compare:

• Я добавляю сливки в соус. = I add cream to the sauce.
• Сливки уже в соусе. = The cream is already in the sauce.

So:

• в соус = direction/result
• в соусе = location

Because the sentence describes a habitual/repeated action:

• я иногда добавляю = I sometimes add

The imperfective is the normal choice for:

• repeated actions
• habitual actions
• general facts/processes

If you used the perfective добавлю, it would usually refer to a single completed future action:

• я добавлю = I will add

So in this sentence, imperfective добавляю is exactly what you would expect.

The first part, Пусть сливки и довольно густые, functions as a concessive clause or concessive introductory part: although the cream is fairly thick.

Then the main clause follows:

• я иногда добавляю их в соус

Russian normally separates these parts with a comma, just as English usually separates although... clauses from the main clause.

So the comma marks the boundary between:

1. the concession
2. the main statement

Yes, Russian word order is flexible, though each version may sound slightly different in emphasis.

The given sentence is natural because it starts with the concession:

• Пусть сливки и довольно густые, я иногда добавляю их в соус.

You could also rearrange parts for emphasis, for example:

• Я иногда добавляю сливки в соус, пусть они и довольно густые.

That still means something like:

• I sometimes add cream to the sauce, even though it’s fairly thick.

The original order is good if you want to foreground the although/even though idea first.