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Pear trees vary in whether they are self-pollinating or require a second variety for cross-pollination. "Unless you purchase a tree with two compatible varieties grafted onto a single rootstock, you will need to plant two different, compatible types of pear in order to obtain any fruit. Check with the nursery where you purchased your tree or your local extension office to ensure that the trees you select can pollinate each other."

This is most probably pear rust. This article may help: https://www.gardeningknowhow.com/edible/fruits/pear/pear-rust-mite-damage.htm

Proper watering of a newly planted tree is very important. Daily watering for the first 2 weeks.
Do the branches snap off or do they bend? If they snap off the tree has likely died.

The shoots growing from the base of the tree are growing from the root stock. What type of tree that was used in likely not a Pear tree.

Here is a few links.
https://www.gardeningknowhow.com/ornamental/trees/tgen/watering-newly-planted-tree.htm
https://www.gardeningknowhow.com/edible/fruits/pear/growing-pear-trees.htm

Dwarf Pear trees can be planted as far apart as 200 feet and as close as 15 feet.

Full size Pear trees should be planted at least 20 feet apart and no more than 200 feet.

I'm sorry you lost your Pear Tree.
I do know that the long harsh winter that most of the United States suffered effected gardens quite a bit.
Tree loss has been a common complaint here at Gardening Know How. Branches that snap are dead but if they bend there is still a possiblity the tree is alive.

The shoots growing at the base are likely growing from the root stock as most Pear Trees sold for home gardens are from grafted stock.
The shoots will not grow into another Pear tree.

I would dig up the root and remove.
Remember that garden loss makes for new opportunities.

This article should help: https://www.gardeningknowhow.com/plant-problems/pests/get-rid-squirrels.htm