I'm a software engineer and I searching for a homelessremote job because I would like to travel a lot.

While I understand what you mean by homeless, I think the image of ‘homeless’ (people who live on streets or in parks) is too strong. Remote is better.

If someanyone knows of an company who propose a homeless jobis looking for remote employees, I'll letgive you my contact information.

You might also say ‘contract freelancers’

Searching for a homeless jRemote Job (fFake aAnnouncement)

I'm a software engineer and Iam searching for a homelessremote job because I would like to travel a lot.

If someone knows an company who propose a homeless jobthat has openings for remote work, I'll letgive you my contact information to forward.

I'll be very happy! would be ecstatic!

Searching for a homelessremote job (fake announcement)

Correction based on context. I'm assuming that by 'homeless job', you mean jobs that are done from home. Those are called remote jobs.

I'm a software engineer and I searchwho is looking for a homelessremote job because I would like to travel a lot.

Rather than having 2 separate sentences joined by an 'and', the sentence would be more cohesive if you make it into one sentence. If you prefer the first way, just correct the 'I searching' to 'I'm searching' and 'homeless job' to 'remote job' and you should be good to go.

If someoneyou knows of any company who propose a homelessthat is offering remote jobs, I'll let you myfeel free to contact me.

A much nicer and formal way to put the same sentence. Here's the breakdown:
1. You don't use 'an' before company because the word 'company' starts with a consonant.
2. Rather than using 'someone knows', using 'if you know' is more direct in phrasing.
3. 'Offer' is a better word to use than 'Propose'. You propose to your girlfriend. You propose a plan. You offer a snack. You offer a job.

I'lld be very happy!happy to reply.

Just a bit formal way to end it.

Searching for a homelessremote job (fake announcement)

Homeless is about a person who has nowhere to live, I think you mean a remote job? A remote job (also called a work-from-home job) is one where you work from someone that is not a fixed office.

It's also possible that this is meant as a joke, but it doesn't land if so.

I'm a software engineer and I searching for a homelessremote job because I would like to travel a lot.

If someone knows an company who propose a homelesshas remote jobs, I'll let you know my contact details.

I'll be very happy!

As written, this statement is just a bit disconnected from the rest of the piece. I think it would be better if you clarify if it's receiving information that would make you happy, or actually being hired for the position.