Can I storage baggage for some hours?

Take your bag with you... grab a free shuttle to Union Station. Get a locker there.

Storaging baggaging is as simple as asking a bagger storer to store your bags. Go to the baggage storage store for bags and it’ll be taken care of.

Not at all. I asked my friend who works there and they told me that airlines do not allow storage of bags even in their baggage offices due to security. There is no such fee like someone else mentioned. Some airlines will let you check your bags in early- so paying the baggage fee to check your carry on might be worth it if you can check it in early. This way you can take the metro down town, or anywhere else you want to go without having to drag a suitcase around.

There are no public lockers at Union Station

No

It will be that a virus test is necessary to travel to Houston