First off, I always suggest Google Tag Manager if you have the ability to install it - it makes changing and adding tracking later much easier. With GTM you put one block of code on every page once, and then within GTM you can set up all the different actions you want to track, and you can limit the tracking to a single page, a set of pages, or have it everywhere the GTM code is.
The one thing to remember if you haven't used GTM is that it doesn't do any tracking automatically - even pageviews have to be created as a tag/trigger pair.
Unfortunately, connecting organic search keywords to activity on your site is difficult. Without Google Search Console, it might be impossible, and even with Search Console it is very limited. I have not found a way to tie keywords to conversion rates for goals - or to much of anything, actually.
However, you can still get at conversion rates for these individual forms. Let's run through the options.
You could set up a goal for each page with a destination of the thank you page and a funnel consisting of viewing the individual profile page, marked "required." The overall conversion rate and total number of conversions for every one of these goals will be the same, because every visit to the destination page is a goal conversion, whether or not the visitor went through the funnel. However, in the Conversions > Goals > Funnel Visualization report, you will be able to see the rate at which people got from the profile page to the thank you page. You would just have to visit that report for each goal individually.
For this, you would set up an event tracking each of the form submissions - Google Tag Manager would be very helpful for this, because you could create a variable that reads some kind of identifying label off the profile page and sends it as the event label (it could even be the page path), so you have to set up only 1 event trigger/tag pair in GTM to track all of the forms. (Just make sure you're not sending anything that will look like Personally Identifiable Information to GA!) Then you would set up a goal for each page. Unlike in option #1, it would not be easy to get a submissions per pageview conversion rate, but the total goal completions and conversion rate (submissions per session) would be broken out per profile page.
The goal approach of these first two options is only practical if you have no more than 20 profile pages. If you do want to use goals I would recommend creating a View just for those goals to live in, so they are not taking up your limited goal slots in the main View.
Events and your own calculations.
I think this is going to be the best long-term solution to your tracking needs. You'll set up a collection of events as in #2 but no goals (page path as event label for the form submission event might be most convenient here). Then I would recommend the Google Sheets add-on for Google Analytics for computations. Pull in the form submission events with their labels, the total number of sessions, and the total number of pageviews for each of the profile pages. Then in another tab of the spreadsheet you can create your own report of form submission data: total number of submissions, submissions/pageviews per profile (this is where having event label = page path would be helpful), submissions/sessions. You can set it up so the report always uses a certain date range relative to "today" and refreshes overnight, or you could have the report configuration read the date range from the custom report tab, and run the report manually.
Any of the options is going to take some time to set up, but after that you'll be able to do your ongoing reporting without too much extra effort each time.