verbs + te + infinitive or + om + te + infinitive

[logicgate]

What is correct or most correct?

>Ik wil je niet dwingen om tafelzout te eten.

>Ik wil je niet dwingen tafelzout te eten.

What is the rule : are some verbs used indifferently with or without om ? Do some verbs require one of both forms ?

[LeSNT2]

Yes, some verbs can use 'te' as well as 'om ... te...'. There are also verbs that can only use 'om ... te...' or can only use 'te'. I think this website will help you: https://zichtbaarnederlands.nl/nl/zinsbouw/te (in Dutch) https://zichtbaarnederlands.nl/en/syntax/te (in English).

[logicgate]

From the list of verbs

beginnen te
blijken te
besluiten te
durven te
niet hoven te
lijken te
proberen te
verbieden te
vergeten te
weigeren te

at least proberen and vergeten seems to be possibly constructed with te or om te. What verbs from this list are with te only and which ones are with te or om te ?

If you are courageous same question for the list

chten
(be)horen
beloven
beogen
bevelen
beweren
denken
dienen
dreigen
dwingen
eisen
gebieden
gelasten
geloven
hopen
komen
leren
menen
plegen
pogen
schijnen
trachten
vallen
verklaren
verlangen
verplichten
verzuimen
vinden
vóórkomen
vragen
vrezen
wagen
wensen
zeggen
zien
zijn

(and is there any difference in meaning?)

[LeSNT2]

A short summary:

We use om ... te ... if there is some sort of goal. For example: Ik ga naar het park om te fietsen. (I go to the park to cycle, cycling is the 'goal')
We use om ... te ... if there is more information about the adjective. For example: Het is vervelend om af te wassen. (It's annoying to do the dishes, doing the dishes gives more information about the adjective 'vervelend')

We use te if we use positionverbs like 'staan', 'liggen', 'zitten' or 'lopen'. For example: Ze staat een boek te lezen. (She's reading a book while standing)
We use te with certain verbs like 'beginnen', 'blijken' or 'besluiten'. For example: Ik besluit naar links te gaan. (I decide to go left)

About your lists:

beginnen te
blijken te
besluiten te
durven te
niet hoven te
lijken te
proberen te
verbieden te
vergeten te
weigeren te

at least proberen and vergeten seems to be possibly constructed with te or om te. What verbs from this list are with te only and which ones are with te or om te ? Yes, you can use om te as well as te with the verbs proberen and vergeten. The verbs beginnen, durven, hoeven and lijken can only use te and can't use om te.


achten
(be)horen
beloven
beogen
bevelen
beweren
denken
dienen
dreigen
dwingen
eisen
gebieden
gelasten
geloven
hopen
komen
leren
menen
plegen
pogen
schijnen
trachten
vallen
verklaren
verlangen
verplichten
verzuimen
vinden
vóórkomen
vragen
vrezen
wagen
wensen
zeggen
zien
zijn

In this list the verbs beloven, beogen, bevelen, dreigen (only if a person is the subject), dwingen, gebieden, gelasten (only if a person is the subject), leren, pogen, trachten, verlangen, verplichten, verzuimen, vragen, wagen en wensen can use te and om te. The other verbs can only use te.

(and is there any difference in meaning?) No, there is no difference in meaning. For example: Ik weiger te verklaren dat ik het heb gedaan. and Ik weiger om te verklaren dat ik het heb gedaan. Both have the same meaning: I refuse to declare that I dit it.