We don't step onto a scale to measure our weight and think, "oh, where's the moon, so I can compensate for its effects".

No... the tidal forces won't change your performance.

It depends whether you want the vertical or horizontal component of the force.  Common sense tells me the vertical component should be greatest when the attracting body is on the meridian, the horizontal when it's rising or setting.

The sun crosses the meridian at local noon.  The mean period between successive lunar transits is 1.0350501 days, but it varies quite a bit (la luna e mobile).  See the book Astronomical Algorithms by Jean Meeus.  His English is sometimes a bit quaint but his maths are generally sound (I did find a confusion between sin and cos in one formula in an early edition).  The same book will tell you how to calculate the times of sunrise & sunset, moonrise & moonset.  I suspect that for your purpose you could ignore the effects of refraction and parallax, and so simplify the formulae.