Aw ni ce! I don’t really quite understand when to use bɛ ka because the progressive can also be formed using just ‘bɛ’.
A bɛ ji min.
She is drinking water.
Muso bɛ tobili la.
The woman is cooking.
Nin muso in bɛ ka mun tobi?
What is this woman cooking?
A bɛ ka sonnerie.
It’s ringing. (telephone)
Is there a certain rule of thumb to remember as to when one should use ‘bɛ ka’?
Nba! I ni ce! 
(The predicate marker bɛ ka in the AKT dictionary is currently here under kà since it is written as two words and one needed to be the “head”.)
The short answer is that there are multiple potential ways to express what English expresses specifically with the progressive tense (e.g., I am going instead of I go). All of your examples are right (except for maybe the one with sonnerie, for which I would have put sonner [the French verb for ‘ring’]) and here’s how the break down:
bɛ = the imperfective predicate marker; this can also have a habitual meaning (e.g., À bɛ ji min ‘He/she drinks water’)bɛ NOUN la = the situative plus a noun and postposition (lit. ‘I am in NOUN’)bɛ ka = a progressive predicate marker combining bɛ and the infinitive marker ka, which is written separately by convention typicallyThere is actually one more (especially in Jula-speaking areas):
bɛ ... VERB-la = the imperfective predicate plus a suffix on the verb
(See this blog post on Speech Events that I wrote years ago for an investigation between the differences between this progressive form and the bɛ NOUN la one list above)
The choice of which form to use most often, in my experience, hinges a lot on regional preference and community. So I would listen to the people around you, try out the different forms and see which one works best. The only one that might give people pause is if you use the simple bɛ form since it can also have a habitual meaning, so perhaps to opt to others if you are 100% sure of your desire to express what is a progressive in English.
Nse! Thanks @coleman!! 
This is nice to finally understand. As I have been corrected, more than once, when I used bɛ instead of bɛ ka. For a minute there I thought I had the wrong understanding of when and how bɛ can also be used. 
It seems that the community preference here is bɛ ka. 
So am I understanding correctly that bɛ ka is interchangeable with bɛ (in the progressive tense) regardless of sentence structure?
A bɛ ka ji min.
She is drinking water.
Muso bɛ ka tobili la.
The woman is cooking.
Nin muso in bɛ mun tobi?
What is this woman cooking?
A bɛ sonner.
It’s ringing. (telephone)
And thanks for sharing how to find bɛ ka in the An ka taa dictionary! Because I did check there but I wouldn’t have even thought to look up ka! And I also wondered what the ka (infinitive marker) part was too! And you have also answered that!! 
I ni dɔnniya, karamɔgɔ!
This one doesn’t work because Muso bɛ tobili la is not a verbal sentence. The bɛ in this case is a situative:
Muso bɛ tobili la
woman + located.in + act.of.cooking + in‘The woman is cooking’
Could you say:
Muso bɛ ka tobi kɛ
No. You say:
Muso bɛ ka tobili kɛ
The verb is k’à tobi.
If there are more questions about specific examples and whether they are possible, please make a separate topic for those expressions. Here’s instructions on how to reply as a linked topic.
Noted thanks!