InfoPath Dev

I have created a SP 2010 site, with web pages, libraries, and lists, on one physical server as my production database. Is it possible to make a copy of all of this and move it to an Office 365 SharePoint 2013 on-line account, as a development practice site?  

 Have you tried saving the site as a template, then uploading it to use in your online site? You may have to do some fix-ups, but it might get you part way there.

 I tried the following instructions, but could not find an option to save site as template. Is it possible this feature has not been activated, and if so can it be - by me?

1. On the Site Actions menu , click Site Settings.

   Note: On a site for which the Site Actions menu is customized, point to Site Settings, and then click the settings that you want to view.

2. On the Site Settings page, in the Look and Feel section, click Save site as template. 

 I just found the following; does it mean, that because I've already published my site, that I cannot save it as a template (the below references 2013, my site is in 2010)?

 

In previous versions you could still save a site as a template when Publishing is turned on by doing it manually.  In 2013 Microsoft closed that loophole. 

There is now no way to save a site as a template with Publishing enabled.  The API will throw an exception as you have seen.  It can't be done. 

So your site is a publishing site, not a team site?

Here's a screenshot of the Site Actions > Save site as template from the Site Settings page of a team site, in case that helps.

 I see your snapshot and raise you one...I'm pretty sure the site is team site, that's been published.

 This is what mine reads. No 'save site as template', option.

 

I'm not familiar with what you mean by a published team site. Your screen shot does not display. It may be that you don't have adequate permissions to save a site as a template.

 

 If this image doesn't show, a copy is attached.

Try your site URL with this added to it (which should get you to the site template save page):

/_layouts/savetmpl.aspx

Apparently if publishing features are enabled, the option is missing: https://blogs.msdn.microsoft.com/richin/2011/12/05/save-site-as-template-option-missing-in-sharepoint-2010/ 

 That got me to the template. However, I got an error message that says I am 'only' logged in as me, and to please choose another log-in (apparently an administrator).

Okay, so it was probably hidden due to permissions. Check with one of your SharePoint Admins, see if they will save it as a template for you & download the template from the gallery so you can upload it to your desired server.