Is Drupal the right CMS for my purpose - need help

You can build forms without PHP. You can include your own PHP as a module. You can insert your own PHP in a page. Everything you list in your requirements is available without using PHP, just install Drupal and add a couple of free add on modules.

My experience of Joomla is that you can add features using free add on module but you quickly need the proprietary "professional" versions of the modules. I build far more complex sites in Drupal without buying a proprietary module.

TikiWiki is find for a wiki about tikis. :-) You can use Wiki markup in Drupal and you get all the extra ways of managing and classifying data including taxonomy, tagadelic, ........., I think there are over 300 modules to choose from.

Themes? Browse http://d-theme.com. 425 themes and new ones arriving every week. All free GPL and downloadable from drupal.org.

One area where Drupal kills the opposition is in the area of permissions. You can have lots of people updating your Web site and complete control exactly what they do. They can have their own page or section or forum without doing anything to anyone else. You can have versions of content and simply wind back the clock if someone does something silly.

Joomla is a better choice than Tikiwiki. When Joomla people use Drupal for a few months, they upgrade to Drupal. Think of Tikiwiki as a Ford, Joomla as a Toyota, and Drupal as a Lexus. Drupal version 7 will be up there with the next generation of space shuttle.

Drupal is fine to setup a community-site. It's one of the use cases that is trumpeted about.

You will want to start thinking in Drupal terms, and to break your content into content types so to speak. You can create your own content types with customizable fields such as date (with calendar functionality), filefield, imagefield, and other content fields.

You can use the views module and a slideshow module to create that slideshow you have currently.

User profiles are extensible via the built-in Profile module or some site developers are using content profile to make user profiles "nodes" or content in Drupal (this makes it easier for some).

Drupal supports phptemplate themes, which means that you can create base page.tpl.php, node.tpl.php, etc... files and customize layout and styling. There's more information in the Documentation section. I can usually move a wordpress theme over to a drupal theme in a couple of hours (by scratch). Others use the zen theme as a base.

See pathauto for automatic user-friendly urls based off of the built-in Path module.

If you need to extend functionality you can do so with your own module. I would suggest taking a look at Drupal's schema and api.drupal.org to familiarize yourself if you plan on delving into this right away. You'll also want to make sure you learn Drupal glossary.