Within Switzerland, the Swiss Travel Pass is valid on all train types and on all major train lines (exceptions do apply for mountain railways). So, yes, the STP is valid on ICE trains.
There is no need to book seats for your journeys. Unless you wish to take a panoramic train (PE), such as the Glacier Express, Bernina Express, or Golden Pass Panoramic where a seat reservation is either mandatory or recommended. For the Luzern-Interlaken Express, a seat reservation is also optional, these trains usually offer enough seats for everyone.
In Switzerland, trains are mass transit like suburban rail in other countries. Therefore, for journeys within Switzerland, optional seat reservations are only possible for trains of category IC, ICE, EC, RJX, and TGV. Yet, not for IR, RE, R, S-Bahn, or S trains.