Welcome here! To get better specific answers to your questions, is your parish reliant on a given hymnal or other worship aid resource for programming and, if so, what? The reason the answer to the question is relevant is because it may limit what you can program.

To give you a couple quick answers to your questions:

1. The past couple years I have done the same hymns between the two.

2. I like it as the recessional, but I know of people who do it for entrance too.

3. At the Lambs High Feast is my go to for communion during the Easter season.

For offertory I always use a hymn called “Festival Canticle”. It goes like this

This Is the Feast of Victory For Our God
Alleluia, Alleluia, Alleluia!

Connor,
I'm late to the party, obviously, but I think I'm going to offer a different perspective than the others who have commented here so far. Take that for what it's worth.

The Easter Vigil isn't Easter Morning. This is one point on which the older practice can be helpful. As a thought experiment, listen to (or read, if you have the training) the Introit for Christmas Eve and Christmas morning. One is mysterious and subdued, while the other is neither. Something similar is at work at Easter, but since there is no Introit, one can't compare these. Easter morning has the Sequence, while the Vigil doesn't.

I wouldn't use the same hymns at both, but then I generally think that duplication should be avoided. I would rather sing less polyphony, for example, than sing the same polyphonic piece for weeks at a time.

The temptation to use the Lutheran rewrite of the Gloria in Excelsis Deo is real, but I encourage you to resist the temptation. I've taught congregations This Joyful Eastertide, among other hymns.

I usually do:

Vigil:
O: the strife is o’er
C: at the lamb’s high feast
R: Jesus Christ is risen today (LYRA DAVIDICA)

Day:
E: the strife is o’er
O: Christ the lord is risen today (LLANFAIR)
C: at the lambs high feast
R: Jesus Christ is risen today

Easter ii:
E: Christ the lord is risen today
O: ye sons and daughters (since Easter ii is the St Thomas gospel)
C: at the lambs high feast
R: Jesus Christ is risen today (since it’s the octave day of Easter)

Repetition doesnt much seem to bother pew sitters.

2. Does Jesus Christ Is Risen Today work better as the entrance hymn or the recessional on Easter Sunday?

How long is your procession? If they're just coming out from the side of the church, why not both? Do several verses coming and the rest going out. If you can do at least 3 verses, make it the pro- and let something else be the re-

I haven't had to organize a Triduum. (We're a TLM in a parish church, and the "main choir" gets to do the NO Triduum) but if I did, I don't think I'd do a lot of repetition. Some days seem to ask for it; the octave of the Nativity has it "baked into the cake" with the repeated Propers, and I repeat some things from Ash Wednesday on Lent 1. But the Vigil isn't one of those days; it's not a "vigil mass" in the sense of "get your Sunday obligation done a day early", but very much its own thing. There's a sense of subdued anticipation: we know something big is happening, but it isn't here yet. Maybe that's why we do the baptisms and confirmations, to let the noobs into the secret before it's here. We've got new fire, we're getting ready, we can't wait. But Jesus Christ ISN'T risen at 10PM on Saturday; we don't know that's happened until dawn on Sunday. So I'd save the big triumphant hymns until then.

What version of VICTIMAE PASCHALI do you use for the Easter Sequence on Sunday? My home parish uses the one found in Breaking Bread, but I like the translation in GIA’s Worship IV more.

We have BB, so I don’t have the luxury of choice!

Here is an Easter text I wrote for the tune RUSSIA---referencing the Cross in procession.
https://forum.musicasacra.com/forum/discussion/19028/god-has-delivered-us-text-for-easter-or-a-pandemic039s-end#Item_3

Connor,

I encourage you to resist the temptation to sing I am the bread of life ever again, in any circumstance whatsoever. Look at what the editors have done to the refrain. Sure, the verses try to quote Holy Writ, but that's not the only prerequisite.

the Sequence is generally sung by a cantor or schola (with active listening by the congregation, of course)

I have to wonder how much my experience of never having done a non-congregational sequence (we even put sheets in the pews for Contemplate the bread of angels, omitted from the hymnal) actually varies from 'normal' NO Masses.