Might be worth letting friends and family know that you're looking for a change. Plenty of employers crying out for staff at the moment. Word of mouth through contacts a big factor for those of us beyond Spring Chicken age.
Never too late to do course/further education to improve your prospects and this is what a Career Guidance Counsellor generally recommends. Tough to make time when smallies and family commitments to deal with but plenty do it and maybe worth making the sacrifice if current situation so grim.
This is true. Always let people know that you're looking for something new. Lots of jobs are not advertised.
If you're thinking of using LinkedIn, there are a few things you can do.
1. Use it to find out about actual jobs. Search for a job title and see how many people are doing that, where, and for whom.
2. If you're unsure what job is good for you, search for skills and see what pops up. I put the entirely generic term 'spreadsheet ' into the search bar and found an ecologist, two project coordinators, and 12 wildly varying job opportunities.
3. If you know what you're interested in doing, make your profile all about that. Use LI to figure out what the keywords for that job are. That will make you easier for recruiters to find you.
4. Subscribe to Google news alerts about the current hot topics in your target sector or companies. If you don't know what those are, look at what they're posting in their socials or on their website (blogs, insights, news).
5. Share an interesting article on that topic one or twice a week, with some comments giving your personal take on that story. Tag relevant groups or people.
6. Comment on posts from your target company(ies) and if you can, share a link that backs up your point, and theirs, in your comment. Don't stalk them though!
7. This should be at the top. Find out who in your existing network can introduce you to a key person in a target company. If someone I know and trust takes the time to introduce someone to me, that person will be the first in the queue when a suitable job opening comes up.
Every now and then I do a bit of profile raising using a few of these and I invariably get recruiters enquiring about me within a week or two.