The driving whilst license was invalid was a traffic misdemeanor which carried only a $202 fine, I'm looking at the register of actions from the court as I type. As this was non-custodial and 4 years old I'm guessing this isn't a huge concern?
The 2018 issue is definitely just a speeding ticket, and there was definitely no arrest or court appearance. However as per my previous post in Texas this still carries a criminal conviction where as in other states it may just be a civil infraction.
I have noticed in the Home Office's "general grounds for refusal" document available on the UK government website it states the following:-
Non-custodial sentences
Where a person has been convicted of or admitted an offence for which they have received
a non-custodial sentence, other than out of court disposal, this is recorded on their criminal
record within the preceding 12 months, paragraph 320(18A) and S-EC.25(a) in Appendix FM
and V 3.5(a) of Appendix V of the Immigration Rules provide for a discretionary refusal of
entry clearance or leave to enter.
You'll notice the highlighted text states this may not be an issue after all? As I would assume it's classed as an out of court disposal?
*edit*
another document from the same place words it this way:-
Paragraph 320(18A) or V 3.5(a) for visitors
You must consider refusing an applicant under paragraph 320(18A) if within the 12
months before the date on which the application is decided, they have been
convicted of, or admitted to, an offence for which they received a non-custodial
sentence, or other out of court disposal that is recorded on their criminal record.
Paragraph 320(18B) or V 3.5(b-c) for visitors
You must consider refusing an applicant under paragraph 320(18B) if in the view of
the Secretary of State:
• their offending has caused serious harm
• they are a persistent offender who shows a particular disregard for the law
If you decide to refuse an applicant on either of these grounds, you must take into
account any human rights grounds and make sure that your refusal is both
proportionate and reasonable.
The two contradict each other however assuming the latter is correct it would be checked against whether the offence caused serious harm or if they are a persistent offender. I guess a speeding ticket wouldn't class as causing serious harm and 2 tickets in 9 years doesn't really class as a persistent offender...