Fleas will not harm your tarantular, since in most cases they are very host speciefic. In your case, fleas from a cat will not suck on tarantula blood (has a very distinctive mixture and is not "warm blooded" and does not run through veins like in mamals.
Do not use bleach for your tank !!!! It will leave mikroscopic paerts of residue that will harm your T.
Unfortunally there is not much you can do except changing substrate and rinsing the tank thourougly with hot water, if you want to clean the tank more intensive you may use liquiod dish detergend like dawn and rinse it of very very very good.
about hardening, your T, as for adults the timeline to be on the save side is 7 days or 1 week, after that time period even the biggest T is completly hard.
If you want to try to handle your T you are good to go.