  Topological flat bands formed in two-dimensional lattice systems offer unique
opportunity to study the fractional phases of matter in the absence of an
external magnetic field. Celebrated examples include fractional quantum
anomalous Hall (FQAH) effects and fractional topological insulators. Recently,
FQAH effects have been experimentally realized in both the twisted bilayer
MoTe2 (tMoTe2) system and the rhombohedral stacked multilayer graphene/hBN
moir\'e systems. To date, experimental studies mainly focus on the first
moir\'e flat band, except a very recent work that reported the evidence of the
integer and fractional quantum spin Hall effects in higher moir\'e bands of a
2.1{\deg} tMoTe2 device. Here, we present the systematical transport study of
approximately 3{\deg} tMoTe2 devices, especially for the second moir\'e band.
At {\nu} = -2 and -4, time-reversal-symmetric single and double quantum spin
Hall states formed, consistent with the previous observation in 2.1{\deg}
tMoTe2 device. On the other hand, we observed ferromagnetism in the second
moir\'e band, and a Chern insulator state driven by out-of-plane magnetic
fields at {\nu} = -3. At {\nu} = -2.5, nonmonotonic temperature dependence of
resistivity and large out-of-plane negative magnetoresistance have been
observed, which likely arises from the frustrated liquid-like ground state and
weak effective Ruderman-Kittel-Kasuya-Yosida interactions. Applying
out-of-plane electric field can induce quantum phase transitions at both
integer and fractional filling factors. Our studies pave the way for realizing
tunable topological states and other unexpected magnetic phases beyond the
first moir\'e flat band based on twisted MoTe2 platform.
