OG 12th, NO.30 and NO.50

Hi guys, im getting a little bit confused on the modifier. Here are the questions:

OG 12th, Question 50,

According to some analysts, the gains in the stock market reflect growing confidence that the economy will avoid the recession that many had feared earlier in the year and instead come in for a "soft landing", followed by a gradual increase in business activity.

followed by a gradual increase in business activity  is modifying the soft landing or the economy?

OG 12th, Question 30,

For members of the seventeenth-century Ashanti nation in Africa, animal-hide shields with wooden frames were essential items of military equipment, protecting warriors against enemy arrows and spears.

protecting warriors against enemy arrows and spears. is modifying the animal-hide shields or military equipment?

Thanks

so actually it depends on the meaning of the sentence?

it might refer to the subject of the sentence and even the noun that is closed to? (sorry,can not type chinese!)

The Olympic Games helped to keep peace among the pugnacious states of the Greek world,proclaming a sacred truce during the festival's month.

Here,what is proclaming modifying? or it is not clear?

Thanks.