When I had only started to learn English, I used to have lessons in a group.

"Used to" is a set phrase that always has the d.

Initially, other students and I tried to give truthfuly information about who we were, where we studied or worked, or what we thought about different points.

"Truly" is an adverb, but here you are describing "information", so you should use an adjective.

IThat was aone reason why we all spoke very slowly.

Or, "That was part of why we all..."

Our teacher noticed ithis and advised us not to talk about ourselves, but spokeeak [or: focus on speaking] using familiar words and grammar that we have gone through.

I remember how I thought that ithat would be really useful tactic.

I know repeating "that" twice can be a bit awkward, but I think it more natural to refer to the tactic with "that."

On theDuring our next lesson, we discussed a finances.

"Finances" is almost always plural. The only exception that comes to mind is when discussing "finance" as an industry, but even in this case, we don't use an indefinite article. For example, "I'm studying finance" or "I work in finance."

Using my teacher’s recommendation, I gave a speech about a huge amount of money that my family kept in an account inat one of the major Swiss banks.

Or, "a huge sum of money"

Eventually after the lesson, people from my class wanted that Ime to gaive them instructions how to open an account inat that bank.

I know nothing about the Swiss banking system that why i. It was so embarrassing.