I was working at home when I thinkought about [the] Arduino.

I looked up Arduino. If I understand correctly it's a platform, so I probably wouldn't use the "the".

When I said about it to my husband, we started to search for an Arduino kit on the Iinternet.

"When I mentioned it" sounds more natural

"started to search for" implies you want to buy one.

I think it might be technically correct to capitalise internet but I rarely see it done.

I'd probably say "search for an Arduino kit online", but what you've written is also correct.

Recently, I tried to create a small mechanisms for fun.

"a", so singular. If you created multiple: "some small mechanisms".

Depending on what you made, "mechanism" might not be the right word.

I'm currently learning about microprocessors architecture, and want to know more about good system design.

I don't know this field so I'm not confident on this, but I think here you'd treat "microprocessor" as an adjective, rather than have it as a possessive.

I was working at home when I thinkought about the Arduino.

When I said about it told my husband, we started to search for an Arduino kit on the Internet.

Recently, I tried to create a small mechanisms for fun.

I'm currently learning a microprocessors architecture, and want to know more about good system design.

I was working at home when I think (thought) about the Arduino.

I was working is past tense. So 'think' has to become 'thought.'

When I said about it told my husband, we started searching for an Arduino kit on the Internet.

For the past tense, you say 'I told.'

Recently, I have tried to create aing small mechanisms for fun.

Recently is a transition word and need a comma after it. Since it is an action that is reoccurring we used present perfect continuous. 'recently I have tried creating..'

I'm currently learning a microprocessors architecture, andthus I want to know more about goodefficient and effective system designs.

Try to use a more advanced word to replace 'good'

I was working at home when I thinkought about the Arduinos.

- You are talking about something in the past (because you wrote 'I was working at home' which is past tense) so you need to use past tense for 'to think' as well
- Bit weird to write 'the Arduino' because there isn't just one of them, there are probably hundreds of thousands of them so it's more natural to talk about them in general here

When I said aboutmentioned it to my husband, so we started searching for an Arduino kit on the Internet.

- Mentioned is a good verb to use in this context here. It indicates something small you say to someone and is more interesting then 'said' which is used a lot and quite bland
- I have added the word 'so' here to join the two phrases. The first part you saying it to your husband lead you to search for it online and the word 'so' indicates that the second part of the sentence happened because of the first part of the sentence

Recently I tried to create a small mechanismscontrapation for fun.

I think contraption is the word you are looking for here. Contraption is a small undefined device that does something

I'm currently learning about microprocessors architecture, and want to know more about good system design.

It's a little bit confusing and I don't have a good explanation for you, this is something you might need to ask an English teacher for but:
- learning about microprocessors architecture is grammatically incorrect
- learning about microprocessor architectureS -> learning about more than one microprocessor architecture
- learning about microprocessor architecture -> learning about microprocessor architecture in general (nothing specific)