Stanza 2 Summary

Get out the microscope, because we’re going through this poem line-by-line.

And think, this heart, all evil shed away,

We've reached the ninth line of the poem, the beginning of the sestet. (The last six lines of a sonnet is called a "sestet"; the first eight are the "octave." For more on this, head on over to "Form and Meter.")
Usually, at this point in a sonnet, the poem starts to shift gears or offer a resolution to problems posed in the octave.
The speaker turns to his addressee again and implores him to "think" (consider, we might say these days) that the soldier's heart "shed away" all the bad stuff of life.
What does this mean? It sounds like the speaker is emphasizing the soldier's goodness, the fact that he eliminated (shed, like old skin—ew) all evil from his life.
Did the first 8 lines pose a problem? Are we getting a resolution here? Or does the poem seem to follow the same tack as before? Let's keep reading…

A pulse in the eternal mind, no less
Gives somewhere back the thoughts by England given;

Come again? A pulse in the eternal mind? What's the deal here, Rupert?!
Well, let's think. The "eternal mind" probably refers to something like the idea of God. The speaker seems to be saying that, when the soldier goes to heaven, he will become part of that larger, unending being and perhaps re-experience, in the form of a "pulse," all the thoughts "by England given."
This probably means that he will re-experience everything he once knew of England—of home—after he dies. So, he's got that going for him.
The speaker says "gives back." Does this mean his thoughts were taken away? Likely, he means that, during some interval between death and heaven, he will not be thinking or conscious, so he'll get his thoughts back once he gets to the Big Man's house.

Her sights and sounds; dreams happy as her day;
And laughter, learnt of friends;

We learn more about what the soldier will experience in heaven. It's almost like he's going to an England in the sky! Celebrate good times!
What will be there when he arrives? Well, the "eternal mind" features the same sights, sounds, and dreams that the soldier enjoyed back in the earthly version of England. There will also be the laughter the solider "learnt of [i.e., from] friends." Plus: cake! Oh wait—
In any case, the speaker paints a very joyous, peaceful picture of life after death that will be much like his happiest times spent in England.

[…] and gentleness,
In hearts at peace, under an English heaven.

This place sounds like a blast. There will also be "gentleness" in the hearts of those who get into this "English heaven." And why shouldn't there be? Their hearts are "at "peace."
This idea of an English heaven is intriguing, though. Do you need a passport? Maybe there are different heavens for different people, and the soldier in this poem will go to an English heaven, as opposed to a German heaven, or a French one. In any case, we know his afterlife will be filled with the familiar comforts of home. Yay for him!