Right. The examples you give are really more to do with a lack of capability to perfrm her job rather than misconduct. Misconduct relates more to matters like theft from employer, using trade secrets, confidentiality breaches, unfitness for duty due to alcohol/drugs, failure to carry out a management instruction within their capability, incompetance or damage to property at work.
The majority of examples you give sounds more like a lack of skill/aptitude to do her job - she's attempting to do her job, but she's doing her job very very badly. Employer may onlydismiss employee's without notice in cases of gross misconduct and must be very careful in doing so because if it is subsequently found that it is not gross misconduct then you will be punished at a tribunal for not following the statutory disciplinary and dismissal procedures in place.
Admitaddly there are some examples you give which sniff of incompetance but because of the risk of an employment tribunal not agreeing that it constituted gross misconduct then I would try discipline her on the ground of a lack of capability to do her job. You can use those examples that border on incompetance in pursuing her for a lack of capability.
I would strongly advise you to follow the statutory disciplinary and dismissal procedures in this case andd so on capability grounds (ie. her lack of skill). ACAS has lots of useful information for employers about taking such disciplanary action, information here:-
Note the guidance notes at the bottom of the web page.
It will probably seem that you are being more reasonable with her than she has any right to expect given her poor job performance but, in the end, it will be you as employer who is likely to suffer if you do not follow them.
If you cannot talk during work I would recommend calling ACAS (it's free) out of office hours on 0845 47 47 47.
You could try talking to her and say that you do not thinking it's working out, she may then offer to resign there and then and it's a problem solved. Otherwise I'd follow the statutory procedure.
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Note the guidance notes at the bottom of the webpage relating to discipline at work.