I thought chlorine would penetrate into the wood and would be difficult to completely wash off. Not true?

The chlorine will evaporate.

today something not very good happened. It was raining and I blew some hulls on my porch so I am sure wild birds were probably coming to the porch to pick up anything they could find. Then I put up aviary and let my birds out. I was in the kitchen where there is a window in the direction of the porch. Then I saw that my birds were on the porch floor foraging among the hulls. I am kind of concerned if they could catch anything bad. not even speaking about wild birds, that's where everybody walks in their dirty shoes. It's raining a lot and we all walk in the backyard bringing some soil onto the porch.

It depends on what's in the dirt - if there are bad germs or anything that's toxic it could cause problems. Cockatiels naturally crave grit so it's likely that they will eat some of the dirt.

a lot of problems.. not even problems but I can't leave them unattended! First of all, some of my birds try to land on the floor on the porch and eat whatever they can find. I sweep the floor before I let them out but when they eat on top of the cage, stuff falls on the floor. I try not to allow it, but sometimes I just don;t see it happening. I am concerned they can get parasites (or something worse). So my concern is possibly bacteria from wild birds and/or parasites. I will need to throw something on the floor
In general, they really enjoy being outside (and their energy increased) but they get too comfortable there. I had two pieces of CEDAR on the window ledge, would never thought they would find it... Two minutes away from that area and I came back to see them sitting there and exploring cedar (I know it's not safe)!

Do you have a cloth tarp you could lay down? When I had guinea pigs I would lay the tarp under their play area so they didn't soil the carpet. Very tightly woven so they couldn't even chew it.

yes, I will have to lay something down... today I was eating out and they told they were out of eggs because of the avian flu. I haven't heard about it this year yet. Now even more worried...

Cedar is unsuitable for nesting material because it's too aromatic for an enclosed nestbox, but it's probably safe enough on an outdoor porch. The open air will prevent the smell from building up.

we had 2 more problems today (of course)
1 - one of my tiels ate ant. We have a few of them crawling on the wooden screen frame that we made for the porch. Not a problem?
2 - they learned to cling the brick wall, crawl on the house wall and eventually trying to eat cement (or whatever) that holds bricks together. Is it dangerous? I provided grit and some of them eat it, but I guess climbing on the wall is more fun. picture of the wall (sorry for that poop again)

Many bird species eat ants, and eating a few of them probably won't harm your birds. I would try to keep the ant population on the porch under control so the birds don't eat a lot of them, and also so the birds won't get bitten by ants.

Whether eating cement is harmful or not will depend on what's in the cement. If they find a brick with a chipped corner they'll probably gnaw on that too. I can't think of an easy solution for that offhand.