approach

1a. This is not the way to approach to the problem.
1b. This is not the way to approach the problem.
2a. Let us go by walk.
2b. Let us walk.
2c. Let us go on foot.
3a. He has left smoking.
3b. He has stopped smoking.
3c. He has given up smoking.
Please correct all.
Thanks.

1a. This is not the correct approach to the problem.
1b. This is not the way to approach the problem.
2a. Let us go for a walk. (walk = noun)
2b. Let us walk.
2c. Let us go on foot. (walk to a specific place, rather than take another form of transport.)
3a. He has quit smoking.
3b. He has stopped smoking.
3c. He has given up smoking.

It is obvious that you want to know if the verb ‘approach’ takes the preposition ‘to’. The answer is NO. However, when it is used as a noun, it does. (Note also that many verbs like ‘tell’, ‘inform’, ‘give’, ‘advise’, answer’ etc do not accept ‘to’ after them as in: ‘Tell/inform him that I am not free now’, ‘Please give him a chance’, ‘I’d advise you not to argue with her’, ‘He answered the question correctly’ etc)

Again, this also is very common among our users. The standard and acceptable phrase is ‘to go on foot’ meaning ‘to go walking’. So I think you could alternatively say ‘Let’s go walking’ (or simply ‘Let’s walk’) which is different (in meaning) from ‘Let us go for a walk’ as you know.

“Our users”
Would those be speakers of Anglophilese?

Only yesterday you were arguing that “native speakers enjoy the freedom to use their language as they like or find it convenient. Others have to stick to the type officially recognized.”
By ‘officially recognised’ I thought you meant standard grammar, but perhaps you just mean that which you choose to use yourself.

Still goading and baiting?

I don’t care, Alan. Everybody knows it. After all, it is due to my additional explanation which satisfies the poster much more or rather fully. I addressed my addition (with explanations and illustrations) to the poster, who did understand what I meant. But you see if someone is determined that something ‘does have to be said about each post’, as the last entry, who can stop that arrogant proclivity?