"General grounds for refusal: considering entry clearance" and probation

I am assuming these rules apply to anyone trying to enter the country regardless of their will/purpose to visit or moving in. Is this correct?

No, this is not correct. From the Immigration Rules which you linked to:

Paragraphs 320 (except subparagraph (3), (10) and (11)) and 322 do not apply to an application for entry clearance, leave to enter or leave to remain as a Family Member under Appendix FM

So if your friend were to apply for a settlement visa based on, for example, his marriage to a British citizen, then the application wouldn't attract an automatic denial on this basis. But settlement visas are outside the scope of this site.

Will probation (not parole) be seen as imprisonment, so my friend will get his visa automatically denied under 2a) ? Or are these lines just for people who got specifically sentenced to prison?

The paragraph you've identified is grounds for mandatory denial. That is, if those conditions apply, the entry clearance officer must deny your friend. Probation is equivalent to a "suspended sentence" in the UK, and since your friend didn't "activate" his sentence, this section doesn't apply. But, if you read further down in the rules, there are these paragraphs:

Grounds on which entry clearance or leave to enter the United Kingdom should normally be refused

...

(18B) in the view of the Secretary of State:

(a) the person’s offending has caused serious harm; or

(b) the person is a persistent offender who shows a particular disregard for the law.

(19) The immigration officer deems the exclusion of the person from the United Kingdom to be conducive to the public good. For example, because the person’s conduct (including convictions which do not fall within paragraph 320(2)), character, associations, or other reasons, make it undesirable to grant them leave to enter.

So does your friend fall under these categories? In the guidance for Entry Clearance Officers, examples of serious harm are offences causing "death" or "serious injury", such as:

• manslaughter
• dangerous driving
• driving whilst under the influence of drink and/or drugs
• the supply of drugs which directly causes the death of an individual
• robbery, particular if the victim is elderly or vulnerable
• arson

If this could apply to your friend, his chance of being granted entry is quite slim.

As for the "persistent offender" rule, the guide gives some qualitative ways in which the Entry Clearance Officer should assess someone who has committed multiple offences, including whether the offences escalated in seriousness, when they occurred, how many where committed, and whether the causes of the offence were addressed (eg, treatment for alcoholism).

Presumably, if your friend had committed several offences, they would all have been over a decade ago. The fact that his offence wasn't activated would be evidence that he has been well-behaved since his prosecution.

As for subparagraph 19, the guidance states this could apply if

• a person is a member of a proscribed group
• a person is suspected of war crimes or crimes against humanity
• a person’s presence is undesirable because of their character, conduct or associations
• a person’s presence might lead to an infringement of UK law or a breach of public order
• a person’s presence may lead to an offence being committed by someone else

Apart from the self-explanatory first two points, this part of the rules is really designed for excluding high profile people who the Home Secretary has decided they don't want to visit. For example, high profile purveyors of hate speech. Almost certainly, it doesn't apply to your friend.

So in conclusion, while probation is not equivalent to imprisonment, and does not attract mandatory exclusion, depending on the offence, the border officer may deny entry on the discretionary grounds. If these discretionary grounds clearly don't apply to your friend, then there is no reason not to apply for a visa, or to seek visa free entry, if they are a US citizen.

Taking your points in order:

1. Leave to enter is permission to "cross the border", which those without a legal right to enter the country require whenever they seek to enter the UK, regardless of purpose.

2. UK terminology divides sentences into custodial (i.e. imprisonment) and non-custodial, with probation one of the more common forms of the latter. With the evidence provided, your friend's criminal record should't automatically cause a visa, entry clearance or application for leave of entry to be rejected. Of course, I am not a lawyer, especially not an immigration lawyer so if your friend is at all worried, he is recommended to consult one.

3. As covered in the comments, the standard rules for a US citizen to the UK as visitor, whether through a visa, entry clearance, or application for leave to enter at the border would limit him to 6 months. Note further that applications can be rejected for multiple reasons, including clearness of intention to leave, means of support and planned activities.