2: that's not how scopes and probes work anyway. The load on the DUT is the quoted probe tip capacitance in parallel with the quoted probe tip resistance.
I found http://www.syscompdesign.com/assets/images/AppNotes/probes.pdf which explains it in pretty easy to understand terms. IIUC from section 5, the probe capacitance can pretty much be disregarded, because the effective probe capacitance (fixed cap + adj cap in series) "must" be 1/9 (for 10x probe) of the scope's input capacitance in order for the probe to be compensated for flat response. So we can calculate capacitance seen at DUT solely in terms of the scope input capacitance = Cs/10.
That seems pretty obviously clear from that doc, but then why do you say it's just the probes quoted capacitance, since clearly (from the doc) that value is irrelevant. But if that value is meaningless, why does every probe even list this spec? EDIT: so that you can make sure it will be compatible with your scope?
The above linked paper is not authoritative. What are that guy's credentials? Just because you read it on the internet, doesn't mean it's true. With that, read on... (tongue in cheek)
The paper you linked implies that the load will see only the series combination of the small probe tip capacitor and the scope input capacitance. Well, that's not true in the real world. In the real world, there are stray/parasistic capacitances to deal with. These add significantly to the overall scope probe load, and account for most of the capacitance seen by the circuit under test.
If the probe specifications say that it presents a load of 10 Mohm in parallel with 10 pF, then that is exactly what the probe tip load is. No guesswork involved. The oscilloscope capactiance has literally no impact on this spec. A scope with a smaller input capacitance and one with a larger one will result in the same probe tip capacitive loading. There is a really good reason for this. For most 10x probe designs, at the BNC connector end of the probe there is a "compensation box" which has, among other things, a small trimmer capacitor in it. This is placed in parallel with the scope's input, so that this capacitor is effectively in parallel with the scope input's capacitance. When you adjust the probe's compensation against the scope's cal output, this is the trimmer you are adjusting
**. Since the capacitance at the probe tip end is fixed, this one needs to be variable, so that the ratio of the (fixed) probe tip capacitance to the scope input capacitance yields the exact same 10x ratio that the resistive components have (10 Mohm : 1 Mohm). This ensures that the low frequency components, which flow mostly through the resistors, and the high frequency components, which flow mostly through the capacitors, are all attenuated by 1/10. This adjustable trimmer cap, when adjusted correctly, ensures that all scope inputs effectively have the same capacitance. Otherwise, the probe couldn't work.
If the 10 pF probe load is too high, you have options. Tek currently makes some passive 10x 10 Mohm probes with about 4 pF capactance, much better. You would need to determine for yourself if they are compatible with your scope (meaning is your scope's input capacitance within the range that can be trimmed by the compensation capacitor). Another option is a Low-Z passive probe, which presents a 1 kohm load to the DUT, but only 1 pF or less. So at very high frequencies (> 30 to 50 MHz), the effective total impedance is lower than so-called High-Z probes. These attenuate by 20x and require a 50 ohm scope input. Going even higher in price you can get into active FET probes.
Tektronix has published good papers on probe theory and design. You can believe what you read in those.
** In some probes, especially cheaper low frequency ones, the compensation trimmer is at the probe end, not the BNC end, but this is much less common in quality probes. In those probes there will be a fraction of a pF difference in probe tip load depending on the the trimmer setting.