You do not (and should not) tell him you are seeing a solicitor first of all. The best approach with someone like this is to grey rock them and only speak to them regarding the children and their needs, as concisely as possible. Is there any way you could redirect any communication through a designated email address rather than engaging in contact over text/phone? I've had to do this with my ex, and he is blocked on social media and WhatsApp - he can call/SMS me in an emergency (when my DS is with him) but cannot contact me for anything else other than by email.
Secondly, a solicitor will guide you through your options. It sounds as if your ex is harassing you with abusive messages, and they may look at putting in place a non-molestation against him which will prevent him from contacting you and using a third party to communicate regarding the children. They may recommend writing to your ex to request that malicious communications cease immediately beforehand.
Normally if there are disagreements about things like childcare arrangements (as in, when the children are with each parent) you will end up needing mediation before it goes to court, unless there is a repeated and sustained pattern of abuse during the relationship and since in which case you can be exempt. Your solicitor should be able to advise you which step is necessary, but you may need to meet with a mediator initially for them to decide whether the exemption is appropriate.
If a mediator decides that mediation is not suitable, yes, the case will go to court where a judge will decide given the evidence about what contact is suitable. Unless there are specific safeguarding issues, this is a relatively easy process whereby the judge will look at what is best for the children.
In regards to child maintenance, if you haven't already, get yourself signed up to the CMS and get them to speak to your ex about his income situation so this is a formalised agreement rather than informal. This is a really quick process and they will ensure that your ex is paying you the correct amount, and if he refuses to pay it, you can notify the CMS who will continue to chase.