Replacing light switch with a 3-way light switch digital timer since light switch can be turn on from another switch. The old light switch has 2 black wires, 1 red wire, and the copper wire (ground) connected to it. How do I know which black wire is Line or Load? And what is the red wire for?

Wrong question. Since the old switch was a 3-way switch the question should be which wire is the common and which are the travlers.
The switch should be marked. Since you have wires and not screw terminals, the red is probably the common
Since you have two 3-way switches you may be asking which switch is the line switch and which switch is the load switch. The line switch is the one that power comes to first.

Power comes to the commen terminal of the first switch, it passes through the switch to one of the traveler terminals, goes on the traveler wires to the traveler terminals of the second switch. There it passes through the second switch to the common terminal and on to the fixture (if the switch settings are the same.)

There is about four different ways a set of 3-way switches can be wired. Without more info we can't tell you which switch is the line and which is the load switch.

The real question you should be asking is does the new timer switch need a neutral.
If the switches are wired with power coming to the switch box you will have a neutral in one of the switch boxes. That will be the line switch. If power is taken to the fixture and a switch leg is used to wire the switches, you will not have a neutral in either switch box.

So first question is does new switch need a neutral.
If switch needs a neutral, the second question is, is power being fed to the fixture or to one of the switch boxes.

The new SunSmart Digital Timer switch does require a neutral which is white. And power is being fed to th fixture.

The line switch will have at least 5 wires (a 2-wire cable and a 3-wire cable). The white of the 2-wire will have voltage on it. It should be connected to the common. One wire of the 3-wire cable should be connected to the black of the 2-wire cable. That wire (of the 3-wire cable) should be connected to the common of the other switch if the travelers do not pass through the ceiling box.
If the travelers pass through the ceiling box that wire could change colors.

How are you going to use this timer? with a relay? Are you only going to use Timer and no 3 way switch at the other end?
You could use a spst relay to control by timer and 3 way, only problem if switch is left in the other condition, when time to go on, it won't.

What is model number of timer?