Ne descurcăm cu această problemă.

Ne is the unstressed reflexive/object form for us / ourselves.

In Ne descurcăm, it goes with the verb a se descurca, which is very often used reflexively. So the idea is not just we manage, but more literally we manage ourselves / we cope.

For a se descurca, the reflexive pronoun changes by person:

• mă descurc = I manage
• te descurci = you manage
• se descurcă = he/she manages
• ne descurcăm = we manage
• vă descurcați = you all / you polite manage
• se descurcă = they manage

Very often, yes, especially in the common meaning to manage, to cope, to get by, to handle things.

So:

• Mă descurc. = I can manage.
• Ne descurcăm. = We can manage / We’re coping.

Romanian uses the reflexive form here where English usually does not.

There are also non-reflexive uses of a descurca, but for a learner, the important everyday pattern is the reflexive one: a se descurca.

Descurcăm is 1st person plural present tense, so it means we manage / we cope.

It comes from a se descurca:

• eu mă descurc
• noi ne descurcăm

The ending -ăm is a very common marker for we in the present tense for many Romanian verbs.

So:

• descurc = I manage
• descurcăm = we manage

Cu means with, and after a se descurca, Romanian often uses cu to introduce the thing or situation you are coping with or handling.

So:

• Ne descurcăm cu această problemă. means We’re managing with this problem / We can handle this problem.

Other examples:

• Mă descurc cu banii pe care îi am. = I manage with the money I have.
• Se descurcă bine cu copiii. = He/She handles children well.

So cu is the normal preposition here.

Because problemă is a feminine singular noun, and the demonstrative adjective has to agree with it.

Romanian agreement here is:

• acest = this, masculine singular
• această = this, feminine singular
• acești = these, masculine plural
• aceste = these, feminine plural

Since problemă is feminine singular, you need:

• această problemă = this problem

Compare:

• acest lucru = this thing
• această carte = this book

They are related, but they are not used in exactly the same way.

• această is a demonstrative adjective used directly before a noun:

  • această problemă = this problem

• aceasta is a demonstrative pronoun, usually meaning this one / this:

  • Aceasta este problema. = This is the problem.

• asta is a more common, more conversational form of aceasta:

  • Asta e problema. = That’s the problem / This is the problem.

So in your sentence, because a noun follows, această is the correct form.

In this sentence, problemă is simply in its basic singular form. The -ă is part of the noun itself, not a special ending added just for this sentence.

The noun is:

• singular indefinite: problemă
• singular definite: problema

After the preposition cu, Romanian uses the form that looks like the accusative, and for most nouns the nominative and accusative look the same. So here there is no visible case change:

• o problemă
• cu această problemă

So yes, the noun is functioning after a preposition, but the form problemă is the normal one you would expect.

Yes. Romanian word order is fairly flexible, although the most neutral order here is:

Ne descurcăm cu această problemă.

You could also say:

• Cu această problemă ne descurcăm.

That version puts more emphasis on cu această problemă, almost like As for this problem, we can handle it.

In ordinary conversation, the original order is the most straightforward and natural.

No, not in standard Romanian for this meaning.

Because a se descurca is used reflexively, the reflexive pronoun is required:

• Ne descurcăm = correct
• Descurcăm = not correct for we manage / we cope

Leaving out ne would sound incomplete or simply wrong in this context.

A helpful approximation is:

des-cur-CĂM

The stress is on the last syllable: -căm.

About ă:

• ă is a very common Romanian vowel.
• It is a short central sound, somewhat like the a in English about, but not exactly the same.

So:

• problemă ends with that same ă
• această also contains ă

You do not pronounce ă like a full English a in father.

Not exactly.

A se descurca is usually closer to:

• to manage
• to cope
• to get by
• to handle

So Ne descurcăm cu această problemă suggests:

• we can handle it
• we’re coping with it
• we’ll manage with it

If you want the stronger idea we solve the problem, Romanian would more naturally use a verb like:

• rezolvăm problema = we solve the problem

So:

• Ne descurcăm cu această problemă. = We can handle this problem.
• Rezolvăm această problemă. = We solve this problem.

Yes, it is natural and idiomatic.

It sounds like something someone would say when reassuring others that the situation is under control.

Depending on context, Romanian speakers might also say:

• Ne descurcăm. = We’ll manage.
• O să ne descurcăm cu această problemă. = We’ll manage this problem / We’ll handle this problem.
• Putem să ne descurcăm cu această problemă. = We can handle this problem.

Your sentence is perfectly normal and clear.