Could there or could there not be a blackhole in this galaxy and if so or/not, how would you tell? Just wondering.
Just from an image like this, you cannot tell if a galaxy has a (super-massive) black hole (SMBH) at the center of its nucleus or not.
However, a lot of work has gone into this topic, and it seems that most - perhaps almost all - 'normal' (and giant) galaxy have a SMBH; certainly all those with an active galactic nucleus (AGN) do. On the other hand, it's not at all certain what proportion of dwarf galaxies harbor an SMBH. This galaxy looks like a regular spiral, so it almost certainly has an SMBH. Its nucleus looks especially bright, which may be a sign that it's an AGN, or it may be that there's a nuclear star-burst.