Web Hosting /Email forwarding Question

I have a domain name hosted by some company and was getting the site hosting too but did not renew due to management change in the web hosting company.

At present I am managing the site through URL forwarding via a control panel hostname registry company.

I have also created few email addresses and get them forwarded to my other email addresses through the same control panel.

But most of the emails never arrive at my destination address nor returned to the sender - they kind of lost in the cyberspace conveniently by the name registry host I have. When I raise the issue with them, they say it is working and they start working for few days then stops again. They say maybe gone to spam folder of my forwarded email address, when I check the spam box they say if it contains ads it maybe blocked by their email forwarding filters and it sound like another BS to me.

My questions:
Would email forwarding domain name host of mine, deliberately not forwarding them, if they do does it cost them anything at all, so that they don't do it?

What other ways I could get some sort of email hosting free in somewhere else?
or have you experienced a reliable domain name host that does a reliable forwarding I should switch to?

Any reliable free web hosts/email hosts?

is it possible to get an email host somewhere else and keep the domain somewhere else?

RELIABILITY AND YOUR FIRST HAND EXPERIENCE ARE THE MAIN FLAVOR HERE PLEASE

Any suggestions appreciated

All the best

PS ( I have a bit of a credit card payment situation because I deliberately blocked my credit card payments online, so I rather prefer not to deal with paid hosting for a while)