Can I defendant/tenant file UD - 150 counter request to chg date, and/or venue of UD hearing?

You should definitely file the UD-150 Form and state your unavailable dates and reasons for your unavailability, the Court can decide. However, most courts are not going to delay an unlawful detainer trial so you can finish your 90 day probation period. Unlawful detainers are an expedited process. If there are more than a few days of delay need, you should consider offering to deposit the rent with the Court during the delay. Finally, you may want to consider attempting to negotiate a settlement with the landlord or retaining an attorney to do so.