what CMS are you using, usually there are plugins to help you do this. Another alternative is to change the URL back to the old URL but the name stays as the new one - this is a common thing that can happen. But it all depends on your CMS - search its name and 301 redirect, you will get there

Whilst some of it is better than it was, the way it deals with pages is still flawed.

For example most pages are using the url format .au/#!chauffeur-hire-perth/c1ay9

#! is a "hashbang" it means it's being dealt / served through javascript and as such isn't readable via search engines - in addition to this all pages have a canonical of the homepage and so would never rank anyhow...

As much as it may not be what you want to hear, its never likely to rank well - i certainly don't forsee it ever ranking in the top 3... sorry

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Being transparent: I have never been one to support the likes of WIX or others of a similar nature. The templates they use are built to cover so many bases that it will never really please anyone completely. Also the way in particular WIX deals with pages is concerning in particular - others do it too i should add.

sorry to be the messenger of bad news.

would be good to get .com/category/name if possible

obviously if you do that becareful about using canonical urls as things may appear in more than one cat

screaming frog is your best bet

in terms of categories, they are more reference points than definite areas, that is why you can actually input anything you want into there. so yes taxi is a go-er

the difference between the two is that one dictates you saying "we serve within 5 miles radius" it includes every city and town in that area... the second says we only serve this town or city ... (state country etc). the radius is more for local businesses and locations for companies who have multiple offices or shops.

pointing a folder would involve some DNS changes (to the CNAME record) - i think.

You would be best asking BC - it would be a similar process to pointing a subdomain to BC.

If you host a solution you are not always stuck in time, for example I use things like WooCommerce which is always being updated with new features and gives you great controls.

And just to clarify I am not saying that you cannot do the things YOU may want to do, but there are things that unless you've controls within the server you can't do - like implement GZIP for instance which can be a big deal on big sites.

moving the info site to BC is ok in general.

The reason both EGOL and I recommend having them together and on your own server is that you can control everything (see EGOL's list) and you aren't second guessing the settings on another server which you have no control over. It also means that things like templates can be made much more flexible to meet your exact needs and not just a few of your requirements.

If you can't some how point BC to a folder on your site then moving everything to BC is ok - the other option of course is to set up  a new domain and let it exist in it's own right but you wouldn't get any benefit from that just as you wouldn't from a subdomain.

I think what EGOL means is that switching the domain to your hosting provider means you loose control of certain things within that domain which can be very important to seo. What could be a good compromise here is that you look at putting the shopping cart within a folder on the domain (not a subdomain as this would be a bad move), this means the work you've done on the domain would continue to effect the static info on there and the shop within the folder.

it may not be possible, it depends on your shopping cart provider - if it can't be done then move the domain across and ensure you have redirects in place from old domain links to new ones (eg your about pages redirect).

Hope that helps clear things up