Is it permissible to fast on Thursday, Sha'ban 29th, knowing that astronomical calculations indicate that the first day of Ramadan will be on Saturday?

The twenty-ninth day of Sha'ban is not a day of doubt (yawm al-shakk). The day of doubt is the thirtieth day of Sha'ban if the crescent moon of Ramadan has not been sighted, with the possibility of it being sighted. It is prohibited to precede Ramadan by fasting one or two days, except for those who have a regular habit of fasting. Therefore, fasting on the twenty-ninth day of Sha'ban is permissible if it coincides with your usual fasting practice, such as fasting most of Sha'ban, or fasting on Mondays and Thursdays, or if you connect it to the preceding day. However, if it does not coincide with a regular practice or is not connected to the preceding day, then fasting on it is not legislated.