Your comments

Yes, it does. If you move a file to another directory, you probably want to move it to another directory on the server, too. But Textastic can't know what you want to do in this case, so the link is removed.

To re-establish the link you can upload the file manually using the File Transfer screen.

So it's best to download the file to the correct destination when doing the initial download. 
When you connect to an (S)FTP server, Textastic will use up to three simultaneous connections to speed up file transfers of many files and folders. You can configure this amount in the connection settings screen (setting "Connections"). You can edit a connection's settings by tapping on the blue arrow button on the right side of each connection.

Since Version 3.1 all connections are automatically closed after a file transfer is complete.
Thanks for your detailed description.
Please try to enable the Debug Log setting for the connection and have a look at the log file. You can change the FTP connection settings by tapping on the blue arrow button on the right side of a connection.
Textastic does have search and replace: tap on the loupe icon and then on "Find and Replace".

Edit: ah, you probably meant an iPhone text editor with search & replace, sorry.
Thanks a lot for your feedback.

There are existing discussions for all the points you mentioned. In the future, please search the forum before posting new entries. Each feedback item should cover only one topic.

Here are the relevant existing entries. You can add your vote to them:

2. Import Photos: http://feedback.textasticapp.com/topic/9278-import-pictures-from-the-photos-app/
Currently, files are closed when you switch to another file and the undo history is lost. I'll consider saving the undo history when switching files.
Thanks for letting me know! I'll try to fix it.
You need to select "HTML" as the syntax definition. This is the default for php files.

PHP code inside of <?  ?> or <?php  ?> is then highlighted correctly.