Finding RC time constant with a Y connection
I get a very different number for the time constant, so I don't think you figured the capacitance across the resistor correctly.

The trick to this problem is to redraw it with a logical layout before doing anything else.  Then you just combine parallel and series combinations of capacitors.

Note that one of the capacitors is directly across the resistor.  The total equivalent capacitance can't be any less than that.  Two other capacitors are in parallel, so they just add.

Again, start by redrawing with a logical layout.  Leave the resistor where it is, and draw horizontal lines to the right from its top and bottom leads.  Now fill in the capacitors, drawing them all vertically.  Connect appropriately.  It shouldn't take more than 10 seconds with a calculator to find the total capacitance.