Cu toate că radiografia dentară arată caria, programăm alta.

It means although, even though, or despite the fact that.

Literally, cu toate is something like with all (that), but in this fixed expression cu toate că functions as a conjunction introducing a contrast:

• Cu toate că radiografia dentară arată caria... = Although the dental X-ray shows the cavity...

A very common shorter equivalent is deși.

No. In normal use, cu toate că is followed by a regular finite verb, usually in the indicative, not the subjunctive.

So in:

• Cu toate că radiografia dentară arată caria...

the verb arată is just present indicative: shows.

Because radiografia is definite: it means the X-ray, not just an X-ray.

Romanian usually puts the definite article at the end of the noun:

• radiografie = an X-ray / X-ray
• radiografia = the X-ray

So:

• radiografia dentară = the dental X-ray

This suggests a specific X-ray already known in the context.

Because dentară is an adjective agreeing with radiografia.

Radiografie is:

• feminine
• singular

So the adjective must also be:

• feminine
• singular

That gives:

• radiografie dentară
• radiografia dentară

Compare:

• masculine singular: dinte dentar would not be normal here, but grammatically the adjective would look different
• feminine singular: radiografie dentară

Arată is the 3rd person singular present of a arăta.

Here it means shows, reveals, or indicates.

So:

• radiografia dentară arată = the dental X-ray shows

Because the subject is singular (radiografia), the verb is singular too.

Caria is the definite singular form of carie.

• carie = a cavity, tooth decay
• caria = the cavity, the decay

In dental Romanian, carie can refer to a cavity/decayed spot in a tooth. In this sentence, caria most naturally means the cavity that the X-ray is showing.

Programăm comes from a programa, which often means:

• to schedule
• to arrange
• to book

In a medical context, programăm alta means something like:

• we schedule another one
• we book another one

So the sentence implies arranging another dental X-ray.

Because Romanian often drops the subject pronoun when it is clear from the verb ending.

• programăm = we schedule

The ending -ăm already tells you the subject is we (noi), so noi is unnecessary unless you want emphasis.

• programăm alta = we schedule another one
• noi programăm alta = we schedule another one (with extra emphasis on we)

Because alta means another one, and it replaces the noun radiografie.

So instead of saying:

• programăm o altă radiografie

Romanian can say more naturally:

• programăm alta

Here alta is feminine singular because it stands for radiografie, which is feminine singular.

This is a very important distinction:

• altă = adjective, used before a noun
  
  • o altă radiografie = another X-ray
• alta = pronoun, used on its own
  
  • programăm alta = we schedule another one

So in your sentence, alta is correct because the noun radiografie is omitted but understood.

Because the sentence begins with a subordinate concessive clause:

• Cu toate că radiografia dentară arată caria, ...

Then the main clause follows:

• programăm alta

Romanian normally separates this kind of introductory clause with a comma, just as English does in many similar sentences.

Yes. That would be perfectly natural.

• Cu toate că ... = although / even though
• Deși ... = although / though

Deși is shorter and very common.
Cu toate că can sound a little more explicit or slightly more formal, but both work well here.

Yes. Romanian word order is fairly flexible.

You could also say:

• Programăm alta, cu toate că radiografia dentară arată caria.

This still means the same thing, but the emphasis changes:

• starting with Cu toate că... highlights the contrast first
• starting with Programăm alta... highlights the action first

Both are grammatical.