I'll bem going to the country

"I'll be going" isn't wrong, but "I'm going" is more natural. This is one of those places when the present progressive often used, since you're talking about your future plans.

My girlfriend just invited me to passspend the weekend visiting an acquaintanced of hers, who has a house in the country.

When talking about a specific length of time, you generally say "spend (a few days, the weekend, etc.)" instead of "pass".

I know he has pigs and other animals ion the propriety, terty. That ensures that this experience will be different from the things I'm used to doing.

My girlfriend just invited me to passspend the weekend visiting an acquaintanced of hers, who has a house in the country.

Use 'spend' instead of 'pass'. Also, acquainting is a verb. You would want to use acquaintance here, which usually means someone you just met.

I know he has pigs and other animals ion the proprierty, that ensures that this experience will be different from the things I'm used to do.

Typically, you use the word "in" for buildings or other structures that are inside something. Something out in the open, such as 'property' or 'land', you would want to use the word 'on'.

My girlfriend just invited me to passspend the weekend visiting an acquainted of hers, who has a house in the country.

I know he has pigs and other animals in the proprierty, thatwhich ensures that this experience will be different from the things I'm used to do.

I just hope there'll be an internet connection.

Or, "I just hope there'll be internet."