Those are just the kind of corrections I’m looking for.
It was not clear to me if Te-form transformation is required before using ている for progressive.
If I understood well there is another step. If not please correct me.
| 向か・う | mukau | (verb inf.) |
| 向か・って | mukatte | (TE-form of the verb) |
| 向か・って・いる | mukatteiru | (progressive form, becomes a RU-verb) |
| 向か・って・います | mukatteimasu | (polite form of the RU-verb) |
Or instead the Te-form is not required and does it is possible to transform any verb directly into progressive with ている?
EDIT: the answer is yes. I finally found a section of the Tae Kim grammar where this is explained clearly. The TE-form transformation is only the first step required to add ~いる and transform the verb into a RU-verb. So ~ている (one of the forms of progressive) requires - for the U-verb 向かう (“to sail”) - the transformations steps reported in the table above.
PS: I’m just using this post as an excuse to study Japanese (including errors and corrections). 
EDIT 2 in another grammar (A Dictionary of Japanese Grammar, mentioned) is written:
When TE-verb is a motion verb such as iku ‘go’, kuru ‘come’ and kaeru ‘return’, the meaning of TE-verb ~iru is not ‘be ~ing’. For example, itte iru means ‘to have gone to some place and to still be there’. The following sentences provide examples:
-
次郎はアメリカに行っている。
Jiroo wa Amerika ni itte iru.
Jiro has gone to America and is there. -
ベックさんはもう家に帰っています。
Bekku-san wa moo ie ni kaette imasu.
Mr. Beck has already returned home and is there.
So, following this rule, since ‘to sail’ is a motion verb the rule should apply as well. Consequently, the original sentence should be translated:
- 私たちは港市に向かっています。
watashitachi wa kooshi ni mukatta imasu.
We have sailed to the city (and we are still there).
I’m a little bit confused now.
Probably sailing is not properly a motion verb but a way in which we reached the city.
Can someone more expert than me clarify?
ANSWER (thanks to @Vsotvep):
向かう is not a motion verb, but it expresses a state-of-being, namely the state of being on your way somewhere.