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We report on the hard X-ray burst and the first ~100 days NICER monitoring of the soft X-ray temporal and spectral evolution of the newly-discovered magnetar Swift J1818.0-1607. The burst properties are typical of magnetars with a duration of $T_{90}=10\pm4$ ms and a temperature of $kT=8.4\pm0.7$ keV. The 2--8 keV pulse shows a broad, single peak profile with a pulse fraction increasing with time from 30% to 43%. The NICER observations reveal strong timing noise with $\dotν$ varying erratically by a factor of 10, with an average long-term spin-down rate of $\dotν=(-2.48\pm0.03)\times10^{-11}$~s$^{-2}$, implying an equatorial surface magnetic field of $2.5\times10^{14}$ G and a young characteristic age of $\sim$470 yr. We detect a large spin-up glitch at MJD 58928.56 followed by a candidate spin-down glitch at MJD 58934.81, with no accompanying flux enhancements. The persistent soft X-ray spectrum of Swift~J1818.0-1607 can be modeled as an absorbed blackbody with a temperature of ~1 keV. Its flux decayed by ~60% while the modeled emitting area decreased by ~30% over the NICER observing campaign. This decrease, coupled with the increase in the pulse fraction points to a shrinking hot spot on the neutron star surface. Assuming a distance of 6.5 kpc, we measure a peak X-ray luminosity of $1.9\times10^{35}$ erg/s, lower than its spin-down luminosity of $7.2\times10^{35}$ erg/s. Its quiescent thermal luminosity is $\lesssim 1.7\times10^{34}$ erg/s, lower than those of canonical young magnetars. We conclude that Swift J1818.0-1607 is an important link between regular magnetars and high magnetic field rotation powered pulsars.