Vincenza it does sound from what you say as though you may have a decent case, if that's what you want to do.
In terms of why companies behave in contradiction to their own policies, could be any number of reasons, but yes you are right it will not reflect well on them should this end up in a tribunal.
It sounds as though your letter is being checked by their solicitor. In circumstances where someone has been dismissed at this stage in their employment and is challenging it, then yes it is normal to run it past a solicitor, and doesn't necessarily mean they are planning to offer you some money.
Whether an employer will attempt to settle it would depend on lots of factors. If you decide to put in a tribunal claim they will take advice as to whether it's worth their while defending it or not.
I'm not very clear what help you are asking for. If you have a solicitor already who is familiar with the details of your case and is advising you about whether you can make a claim and for what, keep talking to him/her, he/she is best-placed to advise you.
If it's experiences of a tribunal you are after, there are people who have gone all the way on here, or close to it, so keep bumping and hopefully some people will be able to tell you their experiences.
I hope that's a bit helpful anyway, sorry you are having such a rough time.