Cu cât ne antrenăm, cu atât avem mai multă rezistență.

It is a correlative structure meaning the more ... the more ... or sometimes the more ... the greater ....

So:

• Cu cât ne antrenăm = the more we train
• cu atât avem mai multă rezistență = the more endurance we have

This pattern is very common in Romanian when showing a proportional relationship.

Yes, cu often means with, but in this structure it is part of a fixed expression:

• cu cât = the more / the ...er
• cu atât = the more / by that much

So here you should learn cu cât ... cu atât ... as a whole pattern, not translate cu word by word.

A se antrena is a reflexive verb in Romanian, meaning to train / to work out / to practice oneself.

So:

• mă antrenez = I train
• te antrenezi = you train
• se antrenează = he/she trains
• ne antrenăm = we train
• vă antrenați = you all train
• se antrenează = they train

The pronoun ne is the reflexive pronoun for we. In English, we usually do not say we train ourselves, but Romanian often uses the reflexive form where English does not.

Both are in the present tense:

• ne antrenăm = we train / we are training
• avem = we have

In this kind of general statement, the present tense expresses a general truth or repeated action, just like in English:

• The more we train, the more endurance we have.

Romanian often leaves out subject pronouns because the verb ending already shows the subject.

For example:

• antrenăm already tells you it is we
• avem also tells you it is we

So noi is not necessary unless you want emphasis:

• Cu cât noi ne antrenăm, cu atât avem mai multă rezistență.

This is grammatical, but less natural unless you are stressing we specifically.

Because rezistență is a feminine singular noun, and mult must agree with it.

So:

• masculine/neuter singular: mai mult
• feminine singular: mai multă
• plural: mai mulți / mai multe, depending on gender

Since rezistență is feminine singular, the correct form is:

• mai multă rezistență = more endurance

Here rezistență means endurance, stamina, or resistance in a physical sense.

Depending on context, rezistență can mean different things:

• physical endurance
• resistance to effort
• resistance in a technical or scientific sense

In this sentence, because of ne antrenăm, the natural meaning is physical endurance/stamina.

Both ideas can work, but they mean slightly different things.

• avem mai multă rezistență = we have more endurance
• suntem mai rezistenți = we are more resilient / stronger / more resistant

The original sentence focuses on having more endurance as a quality or capacity. That is why rezistență is used as a noun.

Yes, the comma is standard here because the sentence has two correlated clauses:

• Cu cât ne antrenăm,
• cu atât avem mai multă rezistență.

The comma helps mark the pause between the two parts, much like in English:

• The more we train, the more endurance we have.

Usually Romanian keeps the verb. The full structure is the most natural:

• Cu cât ne antrenăm, cu atât avem mai multă rezistență.

In some contexts, Romanian can shorten repeated material, but for learners it is best to use the complete structure.

Very often, yes. They normally work together as a pair.

Examples:

• Cu cât citești mai mult, cu atât înțelegi mai bine.
  The more you read, the better you understand.

• Cu cât plecăm mai devreme, cu atât ajungem mai repede.
  The earlier we leave, the sooner we arrive.

Sometimes in informal speech the second part may be reduced or rephrased, but the standard pattern is cu cât ... cu atât ....

Good question. In Romanian, cu cât itself already introduces the comparative proportional meaning the more / the ...er.

So even though there is no separate mai in cu cât ne antrenăm, the phrase still means the more we train.

In many other examples, you may see mai inside the clause if the adjective or adverb itself is comparative:

• Cu cât este mai greu, cu atât este mai interesant.
  The harder it is, the more interesting it is.

But with a verb like to train, cu cât alone can carry the idea.

A rough pronunciation for an English speaker would be:

koo kuht neh ahn-treh-NAHM, koo uh-TAHT ah-VEHM mai MOOL-tuh reh-zis-TEN-tsuh

A few helpful points:

• ă is a very short central vowel, like the a in sofa
• ț is pronounced ts
• stress in antrenăm is on the last syllable: -năm
• stress in rezistență is on ten

This is only approximate, but it can help at first.