Looking for a Alarm Clock for Ubuntu with following:
- Repeat an alarm after user defined period of time
- Can be paused
- Can be reset
- Shows a visual indication at alarm time
- Visual indication should remain till it is dismissed by user
Looking for a Alarm Clock for Ubuntu with following:
These 3 should all do what you require:
https://alarm-clock-applet.github.io/
Alarm Clock is a fully-featured alarm clock which resides in the notification area. It is easy to use yet powerful with support for multiple and repeatable alarms, as well as snoozing and a flexible notification system.
Two types of alarms are supported: Alarm Clocks and Timers. Notification is done by either playing a sound or launching an application.
This software is not available in the official repositories. The developers recommend using their official PPA.
sudo add-apt-repository ppa:tatokis/alarm-clock-applet
sudo apt update
sudo apt install alarm-clock-applet
Note: The following part of the answer was written for older versions of Ubuntu, and does not work anymore for Ubuntu 20.04+. If you are using a recent version of Ubuntu, use the PPA mentioned above.

https://apps.ubuntu.com/cat/applications/wakeup/
This package has a complete graphical front end with which a user can set an alarm to wake the computer - from poweroff if possible - and read a user-defined text. This text can grab relevant information (date, time, weather, Evolution schedule and tasks, news from an rss feed, number of new email messages, etc.) and speak that as well, or play music, all as defined by the user. More capabilities can be added to the alarm via a complete and simple plugin system. Supports multiple alarms.

https://apps.ubuntu.com/cat/applications/alarm-clock/
Alarm Clock is the personal alarm clock for GTK+ desktop environments. It supports sound fading, scheduled alarms, snooze option, passive window reminders, exception lists for scheduled alarms, exporting alarms and much more!

By Terminal, you can use this command:
sudo apt-get install alarm-clock-applet
Source: http://www.ubuntubuzz.com/2015/05/how-to-install-alarm-clock-in-ubuntu-1504.html
Budgie CountDown
The icon changes color on time progress, from green to yellow - red.
For 16.04 - 17.10:
Activate backports:
sudo add-apt-repository ppa:ubuntubudgie/backports
and run:
sudo apt install budgie-countdown-applet
For 18.04 and higher, it will be in the repos.
To install alarm-clock-applet in Ubuntu 22.04: https://packages.ubuntu.com/bionic/amd64/alarm-clock-applet/download. I downloaded the amd64 architecture for my system: alarm-clock-applet_0.3.4-1build1_amd64.deb.
$ sudo apt-get install ./alarm-clock-applet_0.3.4-1build1_amd64.deb
Reading package lists... Done
Building dependency tree... Done
Reading state information... Done
You might want to run 'apt --fix-broken install' to correct these.
The following packages have unmet dependencies:
alarm-clock-applet : Depends: gconf-service
Depends: libappindicator1 (>= 0.4.90)
Depends: libgconf-2-4 (>= 3.2.5) but it is not installed
Depends: libunique-1.0-0 (>= 1.0.0) but it is not installed
Depends: gconf2 (>= 2.28.1-2)
E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).
$ sudo apt-get --fix-broken install
"Alarm Clock" application should now be available to run.