Is it possible to send bitcoins to more than one account at the same time?

Yes.

You can also send to more than one address at the same time.

As far as I know bitcoin transfers can only be done into one address.

Not true.

Can I transfer BTC to multiple address at the same time using my own wallet?

That depends on what wallet you are using. Most well written wallets will have this feature.

Do existing wallets on the market have such a feature?

Most do.