Ubuntu – Mysqli for PHP in package thesql

The file is there, only it is another version. It is also present on the release index

-rw-r--r-- 1 lp_publish lp_publish 70366 Aug 26 01:03 php5-mysql_5.3.6-13ubuntu3.1_powerpc.deb

This is probably old apt indexes, you need to download them again, open a terminal and type

sudo apt-get update && sudo apt-get install php5-mysql

Make sure that your package list is updated before trying to install software.

Dynamic link libraries (DLLs) are a Windows-specific technology and don't work on Ubuntu. Because PHP can be run on different operating systems, its configuration files contain examples for how to configure it on different operating systems:

;;;;;;;;;;;;;;;;;;;;;;
; Dynamic Extensions ;
;;;;;;;;;;;;;;;;;;;;;;

; If you wish to have an extension loaded automatically, use the following
; syntax:
;
;   extension=modulename.extension
;
; For example, on Windows:
;
;   extension=msql.dll
;
; ... or under UNIX:
;
;   extension=msql.so
;
; ... or with a path:
;
;   extension=/path/to/extension/msql.so

Normally, the Linux build of PHP already comes with SSL support built in, in contrast to the Windows build, where you need the DLL you mentioned. But you seem to use a third-party build of PHP 7 (maybe a from PPA?), because Ubuntu 14.04 comes with PHP 5 by default. So this third-party build might handle SSL differently.