Yup - the Narva border crossing is in the center of the city, but the bridge is super-congested, so you have to go to the staging area out of town, and only leave it when it's your turn. Otherwise the city would be clogged with stopped traffic, people pissing in the street, etc.
This is the website for the reservation: https://www.eestipiir.ee/yphis/index...uest_locale=en Note: the border queue can fill up quickly, but technically there are 10 minutes set aside in every hour for motorcycles, so you can usually get in even if the car and truck slots are full.
You can also cross south of Lake Peipus, at Koidula/Pechory or at Luhamaa on the Riga-Pskov highway. Those two are far less congested, although not convenient for St Petersburg.
As for insurance, there will be kiosks there to sell you Russian insurance.
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