Before anything else, I would like to express my enthusiasm for the new group fitness classes, asince I have been requesting them for a long time.

Sounds slightly more formal to me

However, I must confess to being rather displeased that the classes have been postponed foruntil next month.

I compreheunderstand how complicated it is to manage the business and coordinate the schedules; nevertheless, I was hoping to start the classes sooner.

“Comprehend” feels like a bit of a strange choice. It's not exactly wrong, but you don't have to go overboard with the formality as it can sound too stiff.

Furthermore, I would also like to ask for theinquire about pricing for the new classes.

Will there be any additional fees or will beare they included in my current membership plan?

“Will be” and “current” don't match tenses

It would behave been helpful to have received this information beforehand.

It's too late to receive this information beforehand. You say “would have been helpful” instead of “would be helpful” because the opportunity for that to happen has already passed.

Additionally, I would like to make onea suggestion for future classes.

Sounds slightly more natural

I strongly believe that you should offer virtual classes for people who can not personally attend so that they can still do exercise from home.

“Strongly believe” is ironically not the strongest of statements but I don't have an alternative in mind at the moment so it’s fine. In formal speech it is generally better to find a stronger adjective than use a modifier like “really” or “very”. For example, in a more formal setting I would prefer “enormous” over “very big”. “Strongly” isn't bad but there are probably better choices.

This maywould increase the number of people interested in applying for the club.

Balance concision and politeness. Also, “would” is more confident, which is good for a proposal. Not required, though

Thank you for taking the time to read my messageyour time and consideration.

^^Very common in business emails

Sergio Lastname

This is probably just because you're online but in a real business email you would of course introduce and sign off with your full name.

My name is Sergio and I am contacting you in regardings to your previous email.

This sounds more natural to me. (US correction)

Before anything else, I would like to express my enthusiasm for the new group fitness classes, since I have been requesting them for a long time.

or,

Before anything else, I would like to express my enthusiasm for the new group fitness classes, since I have been requesting them for quite some time.

However, I must confess, however, to being rather displeased thaabout the classes have beenbeing postponed foruntil next month.

"displeased about" is how we usually use it.

or,

I must confess, however, to being rather unhappy about the classes being postponed until next month.

I compreheunderstand how complicated it is to manage thea business and to coordinate the schedules; nevertheless, I was hoping to startke the classes sooner.

"To comprehend" is very strong and usually used to comprehend whole subject areas.

If you use "start the classes" in this sentence, it sounds as if you're teaching the classes.

Furthermore, I would like to ask for the pricing forabout the cost of the new classes.

Will there be any additional fees or will they be included in my current membership plan?

I strongly believe that you should offer virtual classes for people who can not personally attendattend in person so that they can still do exercise.

"cannot" is one word.

This may increase the number of people interested in applying forto join the club.

Thank you for taking the time to read my messagyour time.

My correction is a standard sentence used in formal mail.

To Whom It May Concern,

This greeting is really formal, and is usually used only when you're not sure who is going to receive and read your email. But based on your next line, it looks like you are responding to an email you received. Even if you don't know who exactly would be reading it, you could check how they signed the email, and then use that. Such as, "Dear staff at YMCA" or "To the manager of [add your gym name here]".

I comprehend how complicated it is to manage the business and coordinate the schedules; nevertheless, I was hoping to start the classes sooner.

Missing an "it" there. Also, I'd suggest using "understand" instead of "comprehend" - I would presume that a business organizing fitness classes might prefer a less academic-sounding communication tone. (But if you personally prefer writing this way, go ahead and keep it.)

Will there be any additional fees or will they be included in my current membership plan?

I strongly believe that you should offer virtual classes for people who can not personally attend so that they can still do exercise.

Exercise works alone as a verb. :)