My opinion.
Curlyleaf pond weed
American pond weed
Eurasian Water Milfoil
Milfoil will be rooted to the bottom of the pond, coontail won't. Too me it looks like you have a long bare portion of stem without leaves that likely runs to the bottom where it is probably rooted. The leaf stems also look paired rather circular.
I added the blue for clarification in what I think it is.
Yes, the Sonar/Fluridone will work. The Curlyleaf Pondweed needs to be treated earlier in the year, before it sets its "turions" or seeds in June/July. Then it dies back on it's own, and the seeds germinate in the late summer/early fall. It stays green under the ice and is the one of the first plants to start growing again in the spring.
Water levels in the pond have to be stable or dropping for treating with Fluridone. AND they have to be stable or dropping for at least 30 days in a row. A 10ppb dose will kill #1 and #3, I wouldn't kill #2, but if you do, a higher dose will be needed. SePRO recommends 45ppb dosage.