Reported speech

Ann asked me whether I had been to Mexico. I answered that I had. Then she wanted to know how long I had been there. I said that I had spent there around 10 days there. Also I told her that I had liked that trip very much. She nodded understandingly and sighed: "I can imagine! I've been to there once, it was an amazing vacation".
"But it was so hot that time", - she said. - "I'm not accustomed to the hot weather very much".
"Neither am I", - I replied. - "But if you're by the sea it's not a problem at all".
Ann agreed.

At that moment my phone rang. It was Andrew, he was asking me if I was going to join him at the week-end and visit a country-side Russian bathhouse ("banya"). I told him that I still had to decide and I would call him in an hour.

Ann asked me who called, and I said that it was a friend of mine, and I would call him back later today.
"Will you?"- she wondered. - "It's five to ten PM already. He might go to the bed soon".
I said not to worry about this as Andrew usually goes to the bed pretty late.

It's five to ten PM - This doesn't sound natural - I would say - It's nine fifty-five pm, which sounds better, or you could just say it's five to ten, as the 2 people having the conversation are both aware that it is evening.

Reported speech

Ann asked me whether I had been to Mexico. I answered that I had. Then she wanted to know how long I had been there. I said that I had spent there around 10 days I had been there around 10 days [or] I had spent around 10 days there. Also I told her that I had liked that trip very much. She nodded understandingly and sighed: "I can imagine! I've been to there once, it was an amazing vacation".
"But it was so hot that time", - she said. - "I'm not really accustomed to the hot weather very much".
"Neither am I", - I replied. - "But if you're by the sea it's not a problem at all".
Ann agreed.

At that moment my phone rang. It was Andrew, he was asking me if I was going to join him on the week-end weekend and visit a country-side countryside Russian bathhouse ("banya"). I told him that I'd had to decide and I would call him in an hour.

Ann asked me who called, and I said that it was a friend of mine, and I would call him back later today.
"Will you?"- she wondered. - "It's five to ten PM already. He might go to the bed soon".
I said not to worry about this (this is not wrong, but it's better to remove it) as Andrew usually goes to the bed pretty late.

"Week-end" and "country-side" are not wrong but it's much more common to write them as one word. Note the fixed expression "go to bed". Excellent work!