It is thought that the number of satellite dwarf galaxies orbiting around Milky Way is counted in hundreds. Are there black holes and neutron stars in satellite dwarf galaxies orbiting around Milky Way and what would be the methods of their detection? Could the probability of having binary massive dense objects (pair of black holes or pair of neutron stars or black hole + neutron star) in such satellite dwarf galaxies orbiting around Milky Way be estimated?
Certainly - as planetmaker pointed out, it would be unlikely for satellite galaxies to lack these objects simply from a theoretical point of view. Let's take the Magellanic Clouds as an example, given how relatively well-studied they are. We know there are massive stars and star clusters in the Magellanic Clouds (R136 comes to mind) and there's no explanation as to how these populations of massive stars could all end their lives as anything but neutron stars and black holes.
Observationally, there are sources of interest in the Clouds that we have directly confirmed to be neutron stars. For example, SN 1987A, the supernova notably also detected in neutrinos, has a central object that we now strongly believe to be a neutron star powering a pulsar wind nebula (Greco et al. 2021) and lies in the LMC. The LMC pulsar PSR J0540-6919 was detected in 1984 (Seward et al. 1984) and subsequently found to be extremely bright in gamma rays (Ackermann et al. 2015) - not that the Clouds are lacking in radio or gamma-ray pulsars (Ridley et al. 2015, Yang et al. 2017). In the radio, the pulsars can all be detected by standard pulsar surveying techniques - observe the source, fold the data at various of trial periods and see if you can find a periodic signal.
Another way to look for these compact objects is to observe x-ray binaries, which have a normal star and a compact object orbiting each other. Mass transfer to the compact object leads to x-ray emission, and you can try to use the flux and spectral properties to determine whether that compact object is a black hole or a neutron star (Lazzarini et al. 2019). Again, there are no shortage of such systems in the LMC or SMC and many probable black hole candidates.
There's also been plenty of interest in the search for an intermediate-mass black hole (IMBH) in the two galaxies, although I believe the evidence so far is indirect and far from conclusive. Some groups have claimed that particular hypervelocity stars originated in the Clouds and were ejected by an IMBH (Galandris & Zwart 2007, Erkal et al. 2019). It's also been suggested that the high velocity of the gas cloud CO-0.40-0.22 can be attributed to an encounter with an IMBH (Ballone et al. 2018), but this is disputed and again indirect.
The same rationale can be extended to the Milky Way's other satellite galaxies, although most are of course less massive and so we'd expect fewer compact objects. If we assume a reasonable Salpeter initial mass function, we find that about 0.26% of stars will produce neutron stars, and about 0.064% of stars will produce black holes. Even a group of only $\sim10000$ stars would be expected to produce half a dozen black holes and close to 30 neutron stars, and we would certainly expect satellite galaxies to produce that many stars over the course of their lives (and obviously many more than that!).
As a final note: I believe the total number of satellite galaxies of the Milky Way is much lower than "in the hundreds", particularly since the kinematics of many have not yet been well-enough established to confirm that they are in fact in orbit around the Milky Way.